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Introduction to Algebra
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Lectures
04:52
Introduction to Trigonometry
Convertbetween Degreeand Radian Measurement
In mathematics, a degree (symbol: Â°) is a unit of angular measurement. It is not an SI unit, as the SI does not specify the measurement of angular distance. The degree is currently used for expressing small angles, due to its practical size, and for expressing the size of an angle in terms of its arc length in many scientific contexts, such as in geometry, trigonometry, and astronomy.
Whitney Dillinger
08:35
Introduction to Trigonometry
Coterminal Angles
In geometry, a cotangent line to a plane curve at a given point is the line that is perpendicular to the tangent line to the curve at that point. The word "cotangent" is derived from the Latin "cotangens", meaning "inverse tangent". The word "cotangent" is sometimes also used to refer to a line that is perpendicular to a radius drawn to the center of a circle or sphere.
Whitney Dillinger
05:18
Introduction to Trigonometry
Draw Anglesin Standard Position
In geometry, a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted .
Whitney Dillinger
05:01
Introduction to Trigonometry
Evaluate Trigonometry Functionsfora Given Point
In mathematics, trigonometry, also called triangulation, is a branch of mathematics concerning the relationships between the sides and the angles of triangles and the lengths of arcs of circles. Trigonometry is used in the measurement of angles, in navigation, in engineering, in physics, and in many other fields. Trigonometry is most simply associated with planar right-angle triangles (trigonometric functions of an angle are then the ratios of the sides opposite that angle). It can also be defined as the branch of mathematics that studies the relationships between the sides and the angles of plane triangles.
Whitney Dillinger
04:46
Introduction to Trigonometry
Find Trigonometry Valuesgivena Quadrantand1 Trigonometry Value
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
04:13
Introduction to Trigonometry
Quadrant Anglesandtheir Trigonometry Functions
In mathematics, the trigonometric functions are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles using the law of sines, and the computation of various other trigonometric functions such as tangent, cotangent, secant, and cosecant. Trigonometry is also used in physics and engineering, for example to calculate the position of a ship at sea from the angles of certain landmarks.
Whitney Dillinger
03:14
Introduction to Trigonometry
Reference Angles
In geometry, a reference angle is the angle between two lines in a plane which intersect to form a triangle. The three angles of a triangle together with the included side are the five parameters which completely describe the triangle, in that they are sufficient to determine the triangle uniquely.
Whitney Dillinger
02:00
Introduction to Trigonometry
Review Special Right Triangles
In geometry, a right triangle or right-angled triangle is a triangle in which one angle is a right angle (90Â°). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The area of a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Whitney Dillinger
09:36
Introduction to Trigonometry
Right Tringle Trigonometry
In mathematics, trigonometry, also called triangulation, is a branch of mathematics concerning the relationships between the sides and the angles of triangles and the lengths of arcs of a circle. Trigonometry is used in the fields of navigation, engineering, physics, and astronomy. Trigonometry is also the foundation of surveying. Trigonometric functions are used to describe the shape of a triangle and the angles between its vertices.
Whitney Dillinger
01:01
Introduction to Trigonometry
Convertbetween Degreeand Radian Measurement - Example 1
A radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement of an angle in radians. The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and radians are now considered an SI derived unit.
Whitney Dillinger
01:19
Introduction to Trigonometry
Coterminal Angles - Example 1
In mathematics, two angles are said to be coterminal if they are in the same half-plane of a Cartesian coordinate system and are separated by an angle of less than pi radians.
Whitney Dillinger
01:32
Introduction to Trigonometry
Draw Anglesin Standard Position - Example 1
In geometry, a Euclidean vector is a geometric object that has magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an "initial point" "A" with a "terminal point" "B", and denoted by AB. A vector is what is needed to "carry" the point A to the point B. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. The concept of vector, as introduced by Bernhard Riemann, is an abstraction of the notion of directed distance function. Vectors can be added to other vectors according to vector algebra, and a vector can be multiplied by a real number, called a scalar, to get another vector. A vector with zero magnitude is called the zero vector.
Whitney Dillinger
02:37
Introduction to Trigonometry
Evaluate Trigonometry Functionsfora Given Point - Example 1
In mathematics and physical sciences, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in the practical solution of triangles, and in many other applications of geometry, such as physics, engineering, and astronomy. Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles. In this case, one usually considers the triangle to be a plane figure, rather than a solid shape. The field of trigonometry was developed extensively in many different directions in early mathematics, before being unified in the modern framework of coordinate geometry. Trigonometry has significant practical applications, for instance in navigation, engineering, physics and astronomy.
Whitney Dillinger
03:23
Introduction to Trigonometry
Find Trigonometry Valuesgivena Quadrantand1 Trigonometry Value - 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
01:49
Introduction to Trigonometry
Quadrant Anglesandtheir Trigonometry Functions - Example 1
In trigonometry and geometry, 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.
Whitney Dillinger
02:25
Introduction to Trigonometry
Reference Angles - Example 1
In geometry, 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.
Whitney Dillinger
02:15
Introduction to Trigonometry
Review Special Right Triangles - Example 1
A triangle is a polygon with three edges and three vertices. A special triangle is a triangle that has certain properties that make it unique.
Whitney Dillinger
04:10
Introduction to Trigonometry
Right Tringle Trigonometry - Example 1
Trigonometry is the study of 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. The 3rd-century astronomers first noted that the lengths of the sides of a right-angled triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all the other angles and lengths can be determined algorithmically. The field of right-triangle trigonometry was developed first, and then trigonometry was unified by studying the reciprocal relationships among the sides and angles of any triangle.
Whitney Dillinger
00:48
Introduction to Trigonometry
Convertbetween Degreeand Radian Measurement - Example 2
A radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement of an angle in radians. The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and radians are now considered an SI derived unit.
Whitney Dillinger
01:15
Introduction to Trigonometry
Coterminal Angles - Example 2
In mathematics, two angles are said to be coterminal if they are in the same half-plane of a Cartesian coordinate system and are separated by an angle of less than pi radians.
Whitney Dillinger
01:33
Introduction to Trigonometry
Draw Anglesin Standard Position - Example 2
In geometry, a Euclidean vector is a geometric object that has magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an "initial point" "A" with a "terminal point" "B", and denoted by AB. A vector is what is needed to "carry" the point A to the point B. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. The concept of vector, as introduced by Bernhard Riemann, is an abstraction of the notion of directed distance function. Vectors can be added to other vectors according to vector algebra, and a vector can be multiplied by a real number, called a scalar, to get another vector. A vector with zero magnitude is called the zero vector.
Whitney Dillinger
02:22
Introduction to Trigonometry
Evaluate Trigonometry Functionsfora Given Point - Example 2
In mathematics and physical sciences, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in the practical solution of triangles, and in many other applications of geometry, such as physics, engineering, and astronomy. Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles. In this case, one usually considers the triangle to be a plane figure, rather than a solid shape. The field of trigonometry was developed extensively in many different directions in early mathematics, before being unified in the modern framework of coordinate geometry. Trigonometry has significant practical applications, for instance in navigation, engineering, physics and astronomy.
Whitney Dillinger
02:53
Introduction to Trigonometry
Find Trigonometry Valuesgivena Quadrantand1 Trigonometry Value - 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
01:59
Introduction to Trigonometry
Quadrant Anglesandtheir Trigonometry Functions- Ex2
In mathematics, the trigonometric functions are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles using the law of sines, and the computation of various other trigonometric functions such as tangent, cotangent, secant, and cosecant. Trigonometry is also used in physics and engineering, for example to calculate the position of a ship at sea from the angles of certain landmarks.
Whitney Dillinger
00:58
Introduction to Trigonometry
Reference Angles - Example 2
In geometry, 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.
Whitney Dillinger
01:43
Introduction to Trigonometry
Review Special Right Triangles - Example 2
A triangle is a polygon with three edges and three vertices. A special triangle is a triangle that has certain properties that make it unique.
Whitney Dillinger
03:27
Introduction to Trigonometry
Right Tringle Trigonometry - Example 2
Trigonometry is the study of 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. The 3rd-century astronomers first noted that the lengths of the sides of a right-angled triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all the other angles and lengths can be determined algorithmically. The field of right-triangle trigonometry was developed first, and then trigonometry was unified by studying the reciprocal relationships among the sides and angles of any triangle.
Whitney Dillinger
00:56
Introduction to Trigonometry
Convertbetween Degreeand Radian Measurement - Example 3
A radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement of an angle in radians. The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and radians are now considered an SI derived unit.
Whitney Dillinger
01:52
Introduction to Trigonometry
Coterminal Angles - Example 3
In mathematics, two angles are said to be coterminal if they are in the same half-plane of a Cartesian coordinate system and are separated by an angle of less than pi radians.
Whitney Dillinger
01:24
Introduction to Trigonometry
Draw Anglesin Standard Position - Example 3
In geometry, a Euclidean vector is a geometric object that has magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an "initial point" "A" with a "terminal point" "B", and denoted by AB. A vector is what is needed to "carry" the point A to the point B. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. The concept of vector, as introduced by Bernhard Riemann, is an abstraction of the notion of directed distance function. Vectors can be added to other vectors according to vector algebra, and a vector can be multiplied by a real number, called a scalar, to get another vector. A vector with zero magnitude is called the zero vector.
Whitney Dillinger
03:27
Introduction to Trigonometry
Evaluate Trigonometry Functionsfora Given Point - Example 3
In mathematics and physical sciences, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in the practical solution of triangles, and in many other applications of geometry, such as physics, engineering, and astronomy. Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles. In this case, one usually considers the triangle to be a plane figure, rather than a solid shape. The field of trigonometry was developed extensively in many different directions in early mathematics, before being unified in the modern framework of coordinate geometry. Trigonometry has significant practical applications, for instance in navigation, engineering, physics and astronomy.
Whitney Dillinger
02:50
Introduction to Trigonometry
Find Trigonometry Valuesgivena Quadrantand1 Trigonometry Value - 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
01:46
Introduction to Trigonometry
Quadrant Anglesandtheir Trigonometry Functions - Example 3
In trigonometry and geometry, 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.
Whitney Dillinger
01:35
Introduction to Trigonometry
Reference Angles - Example 3
In geometry, 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.
Whitney Dillinger
01:38
Introduction to Trigonometry
Review Special Right Triangles - Example 3
A triangle is a polygon with three edges and three vertices. A special triangle is a triangle that has certain properties that make it unique.
Whitney Dillinger
02:28
Introduction to Trigonometry
Right Tringle Trigonometry - Example 3
Trigonometry is the study of 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. The 3rd-century astronomers first noted that the lengths of the sides of a right-angled triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all the other angles and lengths can be determined algorithmically. The field of right-triangle trigonometry was developed first, and then trigonometry was unified by studying the reciprocal relationships among the sides and angles of any triangle.
Whitney Dillinger
00:48
Introduction to Trigonometry
Convertbetween Degreeand Radian Measurement - Example 4
A radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement of an angle in radians. The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and radians are now considered an SI derived unit.
Whitney Dillinger
01:50
Introduction to Trigonometry
Coterminal Angles - Example 4
In mathematics, two angles are said to be coterminal if they are in the same half-plane of a Cartesian coordinate system and are separated by an angle of less than pi radians.
Whitney Dillinger
01:46
Introduction to Trigonometry
Draw Anglesin Standard Position - Example 4
In geometry, a Euclidean vector is a geometric object that has magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an "initial point" "A" with a "terminal point" "B", and denoted by A B. A vector is what is needed to "carry" the point A to the point B. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. The concept of vector, as introduced by Bernhard Riemann, is an abstraction of the notion of directed distance function. Vectors can be added to other vectors according to vector algebra, and a vector can be multiplied by a real number, called a scalar, to get another vector. A vector with zero magnitude is called the zero vector.
Whitney Dillinger
02:30
Introduction to Trigonometry
Evaluate Trigonometry Functionsfora Given Point - Example 4
In mathematics and physical sciences, trigonometry is the study of the relationships between the sides and the angles of triangles. Trigonometry is used in the practical solution of triangles, and in many other applications of geometry, such as physics, engineering, and astronomy. Trigonometry is also the foundation of surveying. Trigonometry is most simply associated with planar right-angle triangles. In this case, one usually considers the triangle to be a plane figure, rather than a solid shape. The field of trigonometry was developed extensively in many different directions in early mathematics, before being unified in the modern framework of coordinate geometry. Trigonometry has significant practical applications, for instance in navigation, engineering, physics and astronomy.
Whitney Dillinger
02:56
Introduction to Trigonometry
Find Trigonometry Valuesgivena Quadrantand1 Trigonometry Value - 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
00:41
Introduction to Trigonometry
Reference Angles - Example 4
In geometry, 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.
Whitney Dillinger
07:59
Introduction to Trigonometry
Review Special Right Triangles - Example 4
A triangle is a polygon with three edges and three vertices. A special triangle is a triangle that has certain properties that make it unique.
Whitney Dillinger
01:36
Introduction to Trigonometry
Right Tringle Trigonometry - Example 4
Trigonometry is the study of 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. The 3rd-century astronomers first noted that the lengths of the sides of a right-angled triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all the other angles and lengths can be determined algorithmically. The field of right-triangle trigonometry was developed first, and then trigonometry was unified by studying the reciprocal relationships among the sides and angles of any triangle.
Whitney Dillinger