Trigonometry

This course involves the study of a very important branch of mathematics called trigonometry. The first section covers how angles are measured and the different units of measurement of angles from unit circle. The second section introduces the different types of trigonometric functions, their definitions, how the values of trigonometric functions can be calculated for a given angle, and how the measure of an angle measure can be determined using trigonometric functions. It also discusses how trigonometric functions can be used to find information about right angles. The third section introduces the definitions and fundamental identities of a trigonometric function, namely, sum and difference formulas, double and half angle formulas, product to sum formulas, sum to product formulas, law of sines and cosines. It also reviews the graph of different trigonometric functions.

15 topics

337 lectures

Educators

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Course Curriculum

40 videos

Powers and Polynomial

25 videos

Rational Numbers

11 videos

41 videos

Exponential Functions

15 videos

61 videos

Parametric Equations

5 videos

Introduction to Vectors

15 videos

15 videos

Polar Coordinates

5 videos

30 videos

Introduction to Conic Sections

23 videos

15 videos

Introduction to Combinatorics and Probability

16 videos

Introduction to Sequences and Series

20 videos

Trigonometry Lectures

Trigonometry

Unit Circle - Overview

In mathematics, the unit circle is a circle with a radius of one. Frequently, especially in trigonometry and geometry, the unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere.

Lily An

Trigonometry

Angles And Measure - Overview

In mathematics, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation.

Lily An

Trigonometry

Angles And Measure - Example 1

In mathematics, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation.

Lily An

Trigonometry

Angles And Measure - Example 2

In mathematics, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation.

Lily An

Trigonometry

Angles And Measure - Example 3

In mathematics, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation.

Lily An

Trigonometry

Angles And Measure - Example 4

In mathematics, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation.

Lily An

Trigonometry

Right Triangle Trig - Overview

In mathematics, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in solving problems in similar triangles, right triangles, triangles presented by their co-ordinates, spherical triangles, and triangles on elliptical arcs. Trigonometry is also used for computing the lengths of the sides of a triangle given one side and the angle opposite that side. Trigonometry is used in navigation, engineering, and physics. Trigonometry is the study of triangles, specifically the relationships between the sides and the angles of triangles. The area of a triangle is half the base times the height. The trigonometry functions are used to relate the sides and the angles of a triangle.

Lily An

Trigonometry

Right Triangle Trig - Example 1

In mathematics, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in solving problems in similar triangles, right triangles, triangles presented by their co-ordinates, spherical triangles, and triangles on elliptical arcs. Trigonometry is also used for computing the lengths of the sides of a triangle given one side and the angle opposite that side. Trigonometry is used in navigation, engineering, and physics. Trigonometry is the study of triangles, specifically the relationships between the sides and the angles of triangles. The area of a triangle is half the base times the height. The trigonometry functions are used to relate the sides and the angles of a triangle.

Lily An

Trigonometry

Right Triangle Trig - Example 2

In mathematics, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in solving problems in similar triangles, right triangles, triangles presented by their co-ordinates, spherical triangles, and triangles on elliptical arcs. Trigonometry is also used for computing the lengths of the sides of a triangle given one side and the angle opposite that side. Trigonometry is used in navigation, engineering, and physics. Trigonometry is the study of triangles, specifically the relationships between the sides and the angles of triangles. The area of a triangle is half the base times the height. The trigonometry functions are used to relate the sides and the angles of a triangle.

Lily An

Trigonometry

Right Triangle Trig - Example 3

In mathematics, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in solving problems in similar triangles, right triangles, triangles presented by their co-ordinates, spherical triangles, and triangles on elliptical arcs. Trigonometry is also used for computing the lengths of the sides of a triangle given one side and the angle opposite that side. Trigonometry is used in navigation, engineering, and physics. Trigonometry is the study of triangles, specifically the relationships between the sides and the angles of triangles. The area of a triangle is half the base times the height. The trigonometry functions are used to relate the sides and the angles of a triangle.

Lily An

Trigonometry

Right Triangle Trig - Example 4

In mathematics, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in solving problems in similar triangles, right triangles, triangles presented by their co-ordinates, spherical triangles, and triangles on elliptical arcs. Trigonometry is also used for computing the lengths of the sides of a triangle given one side and the angle opposite that side. Trigonometry is used in navigation, engineering, and physics. Trigonometry is the study of triangles, specifically the relationships between the sides and the angles of triangles. The area of a triangle is half the base times the height. The trigonometry functions are used to relate the sides and the angles of a triangle.

Lily An

Trigonometry

Graphing Trig Functions - Overview

In mathematics, the sine, cosine, and tangent functions — or, more generally, trigonometric functions — are functions of an angle. The trigonometric functions are commonly used in the study of triangles and modeling periodic phenomena, among many other uses. The most familiar trigonometric functions are the sine, cosine, and tangent. All of them have the value 0 when the argument (angle) is 0. The sine and cosine functions are periodic, with period 2?, while the tangent function is not periodic. The tangent function is, however, continuous, which means that it has a derivative at every point.

Lily An

Trigonometry

Graphing Trig Functions - Example 1

In mathematics, the sine, cosine, and tangent functions — or, more generally, trigonometric functions — are functions of an angle. The trigonometric functions are commonly used in the study of triangles and modeling periodic phenomena, among many other uses. The most familiar trigonometric functions are the sine, cosine, and tangent. All of them have the value 0 when the argument (angle) is 0. The sine and cosine functions are periodic, with period 2?, while the tangent function is not periodic. The tangent function is, however, continuous, which means that it has a derivative at every point.

Lily An

Trigonometry

Graphing Trig Functions - Example 2

In mathematics, the sine, cosine, and tangent functions — or, more generally, trigonometric functions — are functions of an angle. The trigonometric functions are commonly used in the study of triangles and modeling periodic phenomena, among many other uses. The most familiar trigonometric functions are the sine, cosine, and tangent. All of them have the value 0 when the argument (angle) is 0. The sine and cosine functions are periodic, with period 2?, while the tangent function is not periodic. The tangent function is, however, continuous, which means that it has a derivative at every point.

Lily An

Trigonometry

Graphing Trig Functions - Example 3

In mathematics, the sine, cosine, and tangent functions — or, more generally, trigonometric functions — are functions of an angle. The trigonometric functions are commonly used in the study of triangles and modeling periodic phenomena, among many other uses. The most familiar trigonometric functions are the sine, cosine, and tangent. All of them have the value 0 when the argument (angle) is 0. The sine and cosine functions are periodic, with period 2?, while the tangent function is not periodic. The tangent function is, however, continuous, which means that it has a derivative at every point.

Lily An

Trigonometry

Inverse Trig Functions - Overview

In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Lily An

Trigonometry

Inverse Trig Functions - Example 1

In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Lily An

Trigonometry

Inverse Trig Functions - Example 2

In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Lily An

Trigonometry

Inverse Trig Functions - Example 3

In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Lily An

Trigonometry

Inverse Trig Functions - Example 4

In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Lily An

Trigonometry

Equations With Factoring - Overview

In mathematics, factoring is the process of finding factors of a number.

Lily An

Trigonometry

Equations With Factoring - Example 1

An equation is a mathematical statement that two mathematical expressions are equal. In mathematics, an equation is an expression constructed from variables and coefficients that is true for all values of the variables. The variables are also called unknowns. An example of an equation is "x + 2 = 4". The solutions of this equation are the values of x that, when substituted into the equation, make it true. In this case, the solutions are 3 and ?1. The values substituted in are called solutions or answers.

Lily An

Trigonometry

Equations With Factoring - Example 2

An equation is a mathematical statement that two mathematical expressions are equal. In mathematics, an equation is an expression constructed from variables and coefficients that is true for all values of the variables. The variables are also called unknowns. An example of an equation is "x + 2 = 4". The solutions of this equation are the values of x that, when substituted into the equation, make it true. In this case, the solutions are 3 and ?1. The values substituted in are called solutions or answers.

Lily An

Trigonometry

Equations With Factoring - Example 3

An equation is a mathematical statement that two mathematical expressions are equal. In mathematics, an equation is an expression constructed from variables and coefficients that is true for all values of the variables. The variables are also called unknowns. An example of an equation is "x + 2 = 4". The solutions of this equation are the values of x that, when substituted into the equation, make it true. In this case, the solutions are 3 and ?1. The values substituted in are called solutions or answers.

Lily An

Trigonometry

Equations With Factoring - Example 4

An equation is a mathematical statement that two mathematical expressions are equal. In mathematics, an equation is an expression constructed from variables and coefficients that is true for all values of the variables. The variables are also called unknowns. An example of an equation is "x + 2 = 4". The solutions of this equation are the values of x that, when substituted into the equation, make it true. In this case, the solutions are 3 and ?1. The values substituted in are called solutions or answers.

Lily An

Trigonometry

Equations With Factoring - Example 5

An equation is a mathematical statement that two mathematical expressions are equal. In mathematics, an equation is an expression constructed from variables and coefficients that is true for all values of the variables. The variables are also called unknowns. An example of an equation is "x + 2 = 4". The solutions of this equation are the values of x that, when substituted into the equation, make it true. In this case, the solutions are 3 and ?1. The values substituted in are called solutions or answers.

Lily An

Trigonometry

Law Of Sines - Overview

In trigonometry, the law of sines, also known as the law of sines theorem or the law of sin and cosines, is a trigonometric identity relating the sides and angles of a triangle. The law of sines may be derived using the law of cosines and the Pythagorean theorem.

Lily An

Trigonometry

Law Of Sines - Example 1

In trigonometry, the law of sines, also known as the law of sines theorem or the law of sin and cosines, is a trigonometric identity relating the sides and angles of a triangle. The law of sines may be derived using the law of cosines and the Pythagorean theorem.

Lily An

Trigonometry

Law Of Sines - Example 2

In trigonometry, the law of sines, also known as the law of sines theorem or the law of sin and cosines, is a trigonometric identity relating the sides and angles of a triangle. The law of sines may be derived using the law of cosines and the Pythagorean theorem.

Lily An

Trigonometry

Law Of Sines - Example 3

In trigonometry, the law of sines, also known as the law of sines theorem or the law of sin and cosines, is a trigonometric identity relating the sides and angles of a triangle. The law of sines may be derived using the law of cosines and the Pythagorean theorem.

Lily An

Trigonometry

Law Of Sines - Example 4

In trigonometry, the law of sines, also known as the law of sines theorem or the law of sin and cosines, is a trigonometric identity relating the sides and angles of a triangle. The law of sines may be derived using the law of cosines and the Pythagorean theorem.

Lily An

Trigonometry

Law Of Cosines - Overview

In mathematics, the law of cosines is a trigonometric identity relating the lengths of the sides of a triangle to the cosine of one of its angles. It is sometimes referred to as the cosine formula.

Lily An

Trigonometry

Law Of Cosines - Example 1

In mathematics, the law of cosines is a trigonometric identity relating the lengths of the sides of a triangle to the cosine of one of its angles. It is sometimes referred to as the cosine formula.

Lily An

Trigonometry

Law Of Cosines - Example 2

In mathematics, the law of cosines is a trigonometric identity relating the lengths of the sides of a triangle to the cosine of one of its angles. It is sometimes referred to as the cosine formula.

Lily An

Trigonometry

Law Of Cosines - Example 3

In mathematics, the law of cosines is a trigonometric identity relating the lengths of the sides of a triangle to the cosine of one of its angles. It is sometimes referred to as the cosine formula.

Lily An

Trigonometry

Law Of Cosines - Example 4

In mathematics, the law of cosines is a trigonometric identity relating the lengths of the sides of a triangle to the cosine of one of its angles. It is sometimes referred to as the cosine formula.

Lily An

Trigonometry

Double Angle Identities - Overview

In trigonometry, a double-angle (or double-angle) formula is a formula for the trigonometric function of twice an angle. For example, the sine of twice an angle is the same as the sine of the angle and the cosine of twice an angle is the same as the cosine of the angle.

Lily An

Trigonometry

Double Angle Identities - Example 1

In trigonometry, a double-angle (or double-angle) formula is a formula for the trigonometric function of twice an angle. For example, the sine of twice an angle is the same as the sine of the angle and the cosine of twice an angle is the same as the cosine of the angle.

Lily An

Trigonometry

Double Angle Identities - Example 2

In trigonometry, a double-angle (or double-angle) formula is a formula for the trigonometric function of twice an angle. For example, the sine of twice an angle is the same as the sine of the angle and the cosine of twice an angle is the same as the cosine of the angle.

Lily An

Trigonometry

Double Angle Identities - Example 3

In trigonometry, a double-angle (or double-angle) formula is a formula for the trigonometric function of twice an angle. For example, the sine of twice an angle is the same as the sine of the angle and the cosine of twice an angle is the same as the cosine of the angle.

Lily An

Trigonometry

Double Angle Identities - Example 4

In trigonometry, a double-angle (or double-angle) formula is a formula for the trigonometric function of twice an angle. For example, the sine of twice an angle is the same as the sine of the angle and the cosine of twice an angle is the same as the cosine of the angle.

Lily An

Trigonometry

Half Angle Identities - Overview

In trigonometry, a half-angle identity is an algebraic identity involving trigonometric functions of an angle that is half of a given angle.

Lily An

Trigonometry

Half Angle Identities - Example 1

In trigonometry, a half-angle identity is an algebraic identity involving trigonometric functions of an angle that is half of a given angle.

Lily An

Trigonometry

Half Angle Identities - Example 2

In trigonometry, a half-angle identity is an algebraic identity involving trigonometric functions of an angle that is half of a given angle.

Lily An

Trigonometry

Half Angle Identities - Example 3

In trigonometry, a half-angle identity is an algebraic identity involving trigonometric functions of an angle that is half of a given angle.

Lily An

Trigonometry

Half Angle Identities - Example 4

In trigonometry, a half-angle identity is an algebraic identity involving trigonometric functions of an angle that is half of a given angle.

Lily An

Trigonometry

Product Identities - Overview

In mathematics, a product is a mathematical operation that returns a result where the inputs are multiplied together. Product is one of the four basic operations of arithmetic, with the others being addition, subtraction and division. The multiplication symbol, ×, is placed between the two operands. The result is expressed with an equals sign.

Lily An

Trigonometry

Product Identities - Example 1

In mathematics, a product is a mathematical operation that returns a result where the inputs are multiplied together. Product is one of the four basic operations of arithmetic, with the others being addition, subtraction and division. The multiplication symbol, ×, is placed between the two operands. The result is expressed with an equals sign.

Lily An

Trigonometry

Product Identities - Example 2

In mathematics, a product is a mathematical operation that returns a result where the inputs are multiplied together. Product is one of the four basic operations of arithmetic, with the others being addition, subtraction and division. The multiplication symbol, ×, is placed between the two operands. The result is expressed with an equals sign.

Lily An

Trigonometry

Product Identities - Example 3

In mathematics, a product is a mathematical operation that returns a result where the inputs are multiplied together. Product is one of the four basic operations of arithmetic, with the others being addition, subtraction and division. The multiplication symbol, ×, is placed between the two operands. The result is expressed with an equals sign.

Lily An

Trigonometry

Product Identities - Example 4

In mathematics, a product is a mathematical operation that returns a result where the inputs are multiplied together. Product is one of the four basic operations of arithmetic, with the others being addition, subtraction and division. The multiplication symbol, ×, is placed between the two operands. The result is expressed with an equals sign.

Lily An

Trigonometry

Sum and Difference Identities - Overview

The sum and difference identities are a pair of equations in complex analysis that are used to relate the sum and difference of two functions.

Lily An

Trigonometry

Sum and Difference Identities - Example 1

The sum and difference identities are a pair of equations in complex analysis that are used to relate the sum and difference of two functions.

Lily An

Trigonometry

Sum and Difference Identities - Example 2

The sum and difference identities are a pair of equations in complex analysis that are used to relate the sum and difference of two functions.

Lily An

Trigonometry

Sum and Difference Identities - Example 3

The sum and difference identities are a pair of equations in complex analysis that are used to relate the sum and difference of two functions.

Lily An

Trigonometry

Sum and Difference Identities - Example 4

The sum and difference identities are a pair of equations in complex analysis that are used to relate the sum and difference of two functions.

Lily An

Trigonometry

Sum Identities - Overview

In mathematics, summation is an important concept in calculus, and is closely related to convergence of infinite series. It is the process of finding a sum of a finite sequence of numbers. The summation of a sequence of numbers may be defined as the limit of a sequence of partial sums, provided the sequence has a limit. For infinite sequences, the concept of sum is replaced by that of an integral.

Lily An

Trigonometry

Sum Identities - Example 1

In mathematics, summation is an important concept in calculus, and is closely related to convergence of infinite series. It is the process of finding a sum of a finite sequence of numbers. The summation of a sequence of numbers may be defined as the limit of a sequence of partial sums, provided the sequence has a limit. For infinite sequences, the concept of sum is replaced by that of an integral.

Lily An

Trigonometry

Sum Identities - Example 2

In mathematics, summation is an important concept in calculus, and is closely related to convergence of infinite series. It is the process of finding a sum of a finite sequence of numbers. The summation of a sequence of numbers may be defined as the limit of a sequence of partial sums, provided the sequence has a limit. For infinite sequences, the concept of sum is replaced by that of an integral.

Lily An

Trigonometry

Sum Identities - Example 3

In mathematics, summation is an important concept in calculus, and is closely related to convergence of infinite series. It is the process of finding a sum of a finite sequence of numbers. The summation of a sequence of numbers may be defined as the limit of a sequence of partial sums, provided the sequence has a limit. For infinite sequences, the concept of sum is replaced by that of an integral.

Lily An

Trigonometry

Sum Identities - Example 4

In mathematics, summation is an important concept in calculus, and is closely related to convergence of infinite series. It is the process of finding a sum of a finite sequence of numbers. The summation of a sequence of numbers may be defined as the limit of a sequence of partial sums, provided the sequence has a limit. For infinite sequences, the concept of sum is replaced by that of an integral.

Lily An