Graphing Trigonometry Functions

This course primarily focuses on the practical aspect of Graphing trigonometric functions. It talks about the concepts of radians and provides a detailed explanation for the unit circle definition of sine, cosine, and tangent. The course progresses further to calcuate the exact values of the trigonometric functions at different angles and to graph the functions of sine, cosine, and tangent. The course covers the concepts of garphing basic trigonometric functions using transformations. The course ends with the methods to solve trigonometric equations using inverse trigonometric functions.

11 topics

366 lectures

Educators

Course Curriculum

Equations and Inequalities

35 videos

Linear Equations and Functions

20 videos

Linear Equations and Inequalities

28 videos

Systems of Equations and Inequalities

25 videos

Matrices and Determinants

40 videos

Quadratic Equations

10 videos

Quadratic Functions

60 videos

50 videos

Introduction to Trigonometry

44 videos

Applications of Trigonometric Functions

15 videos

Graphing Trigonometry Functions

39 videos

Graphing Trigonometry Functions Lectures

Graphing Trigonometry Functions

Find Exact Trigonometry Functionsof Angles

In mathematics, a trigonometric function is a function of an angle. The function values are related to the angles by trigonometric identities. The most familiar trigonometric functions are the sine, cosine, tangent, and their inverses.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Multiple Transformationsof Trigonometry Functions

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. Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles (those that have one right angle). Such triangles are the only ones that have a trigonometric ratio associated with their angles. Historically, trigonometry was also called "trigonomics" (from the Greek ???????? trig?non, "triangle" and ?????? metron, "measure"). The term "sine" (Latin sinus) was coined by the Dutch mathematician Willebrord Snellius (1591–1626) and was derived from the word "semijunctus" (half-divided).

Whitney Dillinger

Graphing Trigonometry Functions

Solve Equationsusing Inverse Trigonometry Functions

In mathematics, inverse trigonometric functions are functions that take a trigonometric function as an argument and produce a value in the range of the domain of the original trigonometric function. The inverse trigonometric functions are the inverse functions of the trigonometric functions.

Whitney Dillinger

Graphing Trigonometry Functions

Find Exact Trigonometry Functionsof Angles - Example 1

In mathematics, trigonometry, also called triangulation, 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Multiple Transformationsof Trigonometry 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Solve Equationsusing Inverse Trigonometry Functions - Example 1

In trigonometry and mathematics in general, an inverse trigonometric function is a function that is the inverse of another trigonometric function. For example, the inverse sine of an angle is the angle whose sine is that same angle.

Whitney Dillinger

Graphing Trigonometry Functions

Find Exact Trigonometry Functionsof Angles - Example 2

In mathematics, trigonometry, also called triangulation, 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Multiple Transformationsof Trigonometry 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Solve Equationsusing Inverse Trigonometry Functions - Example 2

In trigonometry and mathematics in general, an inverse trigonometric function is a function that is the inverse of another trigonometric function. For example, the inverse sine of an angle is the angle whose sine is that same angle.

Whitney Dillinger

Graphing Trigonometry Functions

Solve Equationsusing Inverse Trigonometry Functions - Example 2

In trigonometry and mathematics in general, an inverse trigonometric function is a function that is the inverse of another trigonometric function. For example, the inverse sine of an angle is the angle whose sine is that same angle.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Multiple Transformationsof Trigonometry 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Solve Equationsusing Inverse Trigonometry Functions - Example 3

In trigonometry and mathematics in general, an inverse trigonometric function is a function that is the inverse of another trigonometric function. For example, the inverse sine of an angle is the angle whose sine is that same angle.

Whitney Dillinger

Graphing Trigonometry Functions

Find Exact Trigonometry Functionsof Angles - Example 4

In mathematics, trigonometry, also called triangulation, 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Multiple Transformationsof Trigonometry 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. Trigonometry is also the foundation of surveying.

Whitney Dillinger

Graphing Trigonometry Functions

Solve Equationsusing Inverse Trigonometry Functions - Example 4

In trigonometry and mathematics in general, an inverse trigonometric function is a function that is the inverse of another trigonometric function. For example, the inverse sine of an angle is the angle whose sine is that same angle.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Horizontal Functions

In mathematics, a horizontal function is a function whose graph is a horizontal line. Such functions are important in the study of differential equations, because any horizontal function is the zero solution of a homogeneous linear differential equation.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Vertical Transformations

In mathematics, a transformation is a rule, operation, or a process that maps elements of one set (the domain) to another set (the range). For example, a linear transformation is a rule that takes a vector in a space and transforms it to another vector also in that space. A vertical transformation is a transformation in which the output is a scalar multiple of the input.

Whitney Dillinger

Graphing Trigonometry Functions

Graphing CSCSECCOT Functions

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x). A function whose domain is a subset of the real numbers is called a "real-valued function". A function from a set X to a set Y is a subset of the Cartesian product X × Y that preserves the ordering, that is, if "x" is in "f" then so is "y" for any "y" in Y. Such a function is called "continuous" if the preimage of every neighborhood of a point "x" in X is a neighborhood of "f"("x") in Y. A function from the real numbers to the real numbers is called a "continuous function". However, most commonly encountered functions in calculus are "discontinuous", which means that they are defined only on a subset of the real numbers.

Whitney Dillinger

Graphing Trigonometry Functions

Graphing Cosine Functions

In mathematics, the cosine function is a trigonometric function that measures an angle's size in degrees. The term "cosine" comes from the Latin word cosinus, which means "the adjacent side". The cosine of an angle is denoted by the symbol or cos. In terms of the standard unit circle, the cosine can be defined as the ratio of the adjacent leg to the hypotenuse of a right triangle, or the ratio of the adjacent side to the hypotenuse.

Whitney Dillinger

Graphing Trigonometry Functions

Graphing Sine Functions

In mathematics, the sine function or sin is a trigonometric function, defined for any angle in the interval (0,2?). It tells us how much the function changes when the angle changes by. It is also known as the "sinus" function in the old German notation.

Whitney Dillinger

Graphing Trigonometry Functions

Graphing Tangent Functions

In mathematics, the tangent function (or tangent) is a function that defines the slope of a straight line, or line segment, at any point along it. The slope of a line is defined as the ratio of the "vertical change" to the "horizontal change" between any two distinct points on the line. The slope of a straight line is constant, and equal to its value at the point where the line is defined, but the slope of a line segment is not constant, and is usually different from the slope of the line at either end of the line segment.

Whitney Dillinger

Graphing Trigonometry Functions

Periodand Amplitudeof Trigonometry Functions

In mathematics, the period of a periodic function is the length of its repeating pattern. The period of a periodic function is the number of full periods of the function. The period of the sine function is the number of radians through which its graph rotates. The amplitude of a periodic function is the maximum distance of the graph from the x-axis.

Whitney Dillinger

Graphing Trigonometry Functions

Unit Circle Revisited

In mathematics, the unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S.

Whitney Dillinger

Graphing Trigonometry Functions

Graph Vertical Transformations - Example 1

In mathematics, a graph transformation is a function that maps one graph to another. Such transformations are used in the study of graph theory, in particular in the study of planar graphs.

Whitney Dillinger

Graphing Trigonometry Functions

Periodand Amplitudeof Trigonometry Functions - Example 1

The period of a periodic function is the time elapsed for a complete cycle. In trigonometry, the period, usually denoted by T, is the length of a circular arc in the unit circle, which is the inverse function of the sine function. The period of a periodic function is the time required for the function to repeat itself. For example, if the period of a function is 2?, then the function repeats itself after every 2? units of time. The inverse function of the sine function is the circular function, which is defined as the length of the arc of the unit circle between the point (1,0) and the point (x,y). The period of a function is a measure of the frequency of the function.

Whitney Dillinger

Graphing Trigonometry Functions

Unit Circle Revisited - Example 1

A trigonometric function is a function of an angle. The angle may be in radians or in degrees. The trigonometric functions are commonly defined for angles in the range –90° to +90°. The commonly-used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cotan), secant (sech), and cosecant (cosech). The inverse trigonometric functions are the arcsine (arcsin), arccosine (arccos), arctangent (arctan), arccotangent (arccotan), arcsecant (arccosec), and arc cosecant (arccosech).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Horizontal Functions - Example 2

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The output of a function f corresponding to an input x is denoted by f(x).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Vertical Transformations - Example 2

In mathematics, a graph transformation is a function that maps one graph to another. Such transformations are used in the study of graph theory, in particular in the study of planar graphs.

Whitney Dillinger

Graphing Trigonometry Functions

Periodand Amplitudeof Trigonometry Functions - Example 2

The period of a periodic function is the time elapsed for a complete cycle. In trigonometry, the period, usually denoted by T, is the length of a circular arc in the unit circle, which is the inverse function of the sine function. The period of a periodic function is the time required for the function to repeat itself. For example, if the period of a function is 2?, then the function repeats itself after every 2? units of time. The inverse function of the sine function is the circular function, which is defined as the length of the arc of the unit circle between the point (1,0) and the point (x,y). The period of a function is a measure of the frequency of the function.

Whitney Dillinger

Graphing Trigonometry Functions

Unit Circle Revisited - Example 2

A trigonometric function is a function of an angle. The angle may be in radians or in degrees. The trigonometric functions are commonly defined for angles in the range –90° to +90°. The commonly-used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cotan), secant (sech), and cosecant (cosech). The inverse trigonometric functions are the arcsine (arcsin), arccosine (arccos), arctangent (arctan), arccotangent (arccotan), arcsecant (arccosec), and arc cosecant (arccosech).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Horizontal Functions - Example 3

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The output of a function f corresponding to an input x is denoted by f(x).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Vertical Transformations - Example 3

In mathematics, a graph transformation is a function that maps one graph to another. Such transformations are used in the study of graph theory, in particular in the study of planar graphs.

Whitney Dillinger

Graphing Trigonometry Functions

Periodand Amplitudeof Trigonometry Functions - Example 3

The period of a periodic function is the time elapsed for a complete cycle. In trigonometry, the period, usually denoted by T, is the length of a circular arc in the unit circle, which is the inverse function of the sine function. The period of a periodic function is the time required for the function to repeat itself. For example, if the period of a function is 2?, then the function repeats itself after every 2? units of time. The inverse function of the sine function is the circular function, which is defined as the length of the arc of the unit circle between the point (1,0) and the point (x,y). The period of a function is a measure of the frequency of the function.

Whitney Dillinger

Graphing Trigonometry Functions

Unit Circle Revisited - Example 3

A trigonometric function is a function of an angle. The angle may be in radians or in degrees. The trigonometric functions are commonly defined for angles in the range –90° to +90°. The commonly-used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cotan), secant (sech), and cosecant (cosech). The inverse trigonometric functions are the arcsine (arcsin), arccosine (arccos), arctangent (arctan), arccotangent (arccotan), arcsecant (arccosec), and arc cosecant (arccosech).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Horizontal Functions - Example 4

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The output of a function f corresponding to an input x is denoted by f(x).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Vertical Transformations - Example 4

In mathematics, a graph transformation is a function that maps one graph to another. Such transformations are used in the study of graph theory, in particular in the study of planar graphs.

Whitney Dillinger

Graphing Trigonometry Functions

Periodand Amplitudeof Trigonometry Functions - Example 4

The period of a periodic function is the time elapsed for a complete cycle. In trigonometry, the period, usually denoted by T, is the length of a circular arc in the unit circle, which is the inverse function of the sine function. The period of a periodic function is the time required for the function to repeat itself. For example, if the period of a function is 2?, then the function repeats itself after every 2? units of time. The inverse function of the sine function is the circular function, which is defined as the length of the arc of the unit circle between the point (1,0) and the point (x,y). The period of a function is a measure of the frequency of the function.

Whitney Dillinger

Graphing Trigonometry Functions

Unit Circle Revisited - Example 4

A trigonometric function is a function of an angle. The angle may be in radians or in degrees. The trigonometric functions are commonly defined for angles in the range –90° to +90°. The commonly-used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cotan), secant (sech), and cosecant (cosech). The inverse trigonometric functions are the arcsine (arcsin), arccosine (arccos), arctangent (arctan), arccotangent (arccotan), arcsecant (arccosec), and arc cosecant (arccosech).

Whitney Dillinger

Graphing Trigonometry Functions

Graph Horizontal Functions - Example 1

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The output of a function f corresponding to an input x is denoted by f(x).

Whitney Dillinger