Cos 180

Using the above proved results we will prove all six trigonometrical ratios of (180° - θ). sin (180° - θ) = sin (90° + 90° - θ) = sin [90° + (90° - θ)] = cos (90° - θ), [since sin (90° + θ) = cos θ] Therefore, sin (180° - θ) = sin θ , [since cos (90° - θ) = sin θ] cos (180° - θ) = cos (90° + 90° - θ) = cos [90° + (90° - θ)] = - sin (90° - θ), [since cos (90° + θ) = -sin θ] Therefore, cos (180° - θ) = - cos θ , [since sin (90° - θ) = cos θ] tan (180° - θ) = cos (90° + 90° - θ) = tan [90° + (90° - θ)] = - cot (90° - θ), [since tan (90° + θ) = -cot θ] Therefore, tan (180° - θ) = - tan θ , [since cot (90° - θ) = tan θ] csc (180° - θ) = \(\frac\) 2. Find the value of tan 120°. Solution: tan 120° = tan (180 - 60)° = - tan 60°; since we know, tan (180° - θ) = - tan θ = - √3 ● Trigonometric Functions • • • Reciprocal Relations of Trigonometric Ratios • • • • • • • • Trig Ratio Problems • Proving Trigonometric Ratios • • • • • • • • • • • • • • Trigonometrical Ratios of (- θ) • • • Trigonometrical Ratios of (180° + θ) • Trigonometrical Ratios of (180° - θ) • Trigonometrical Ratios of (270° + θ) • T • Trigonometrical Ratios of (360° + θ) • • • • • Trigonometric Functions of any Angles • • 11 and 12 Grade Math From Trigonometrical Ratios of (180° - θ) to HOME PAGE

Cos 180 Degrees The value of cos 180 degrees is -1. Cos 180 degrees in radians is written as cos (180°×π/180°), i.e., cos (π) or cos (3.141592. . .). In this article, we will discuss the methods to find the value of cos 180 degrees with examples. • Cos 180°: -1 • Cos (-180 degrees): -1 • Cos 180° in radians: cos (π) or cos (3.1415926 . . .) What is the Value of Cos 180 Degrees? The value of cos 180 degreesis -1. Cos 180 degrees can also be expressed using the equivalent of the given We know, using ⇒ 180 degrees = 180°× (π/180°) rad = π or 3.1415 . . . ∴ cos 180° = cos(3.1415) = -1 Explanation: For cos 180 degrees, the angle 180° lies on the negative x-axis. Thus cos 180° value = -1 Since the cosine function is a ⇒ cos 180° = cos 540° = cos 900°, and so on. Note: Since, cosine is an Methods to Find Value of Cos 180 Degrees The value of cos 180° is given as -1. We can find the value of cos 180 • Using Unit Circle • Using Trigonometric Functions Cos 180 Degrees Using Unit Circle To find the value of cos 180 degrees using the unit circle: • Rotate ‘r’ anticlockwise to form 180° angle with the positive x-axis. • The cos of 180 degrees equals the x-coordinate(-1) of the point of intersection (-1, 0) of unit circle and r. Hence the value of cos 180° = x = -1 Cos 180° in Terms of Trigonometric Functions Using • ±√(1-sin²(180°)) • ± 1/√(1 + tan²(180°)) • ± cot 180°/√(1 + cot²(180°)) • ±√(cosec²(180°) - 1)/cosec 180° • 1/sec 180° Note: Since 180° lies on the negative x-axis, the fin...

Value of Cos 180 The value of cos 180 is equal to -1. Trigonometry is the study of measurements of triangles which deals with the length, height and angles of the triangle. The trigonometric functions have an enormous application in the real world. In various fields like engineering, architecture, satellite navigation, medical imaging and the development of sound waves etc. The functions of trigonometry are widely used by engineers, architects, astronauts to calculate the various measurements that undergo the triangular properties. In some applications, it uses the wave pattern of trigonometric functions to produce the sound and light waves. For the creation of computer music, it uses the wave pattern of sine and What is the Value of Cos Pi (180°)? Value of Cos 180 Degree (π) is -1 How to derive the value of Cos 180 Degrees? The value of cos 180 degrees or the value of cos pi can be represented in terms of different angles like 0°, 90°and 270°. Consider the unit circle in which the Cartesian plane is divided into four quadrants. To find the value of cos 180 degrees from the Cartesian plane, the value 180 degree takes place in the second quadrant. As the cosine values in the second quadrant always take a negative value. From the value of cos 0, we will obtain the value of cos 180°. We know that the exact value of cos 0 degrees is 1 So, cos 180 degree is -(cos 0) which is equal to -(1) Therefore, the value of cos 180 degrees = -1 It is also represented in terms of radi...

Cos 180 Degrees The value of cos 180 degrees is -1. Cos 180 degrees in radians is written as cos (180°×π/180°), i.e., cos (π) or cos (3.141592. . .). In this article, we will discuss the methods to find the value of cos 180 degrees with examples. • Cos 180°: -1 • Cos (-180 degrees): -1 • Cos 180° in radians: cos (π) or cos (3.1415926 . . .) What is the Value of Cos 180 Degrees? The value of cos 180 degreesis -1. Cos 180 degrees can also be expressed using the equivalent of the given We know, using ⇒ 180 degrees = 180°× (π/180°) rad = π or 3.1415 . . . ∴ cos 180° = cos(3.1415) = -1 Explanation: For cos 180 degrees, the angle 180° lies on the negative x-axis. Thus cos 180° value = -1 Since the cosine function is a ⇒ cos 180° = cos 540° = cos 900°, and so on. Note: Since, cosine is an Methods to Find Value of Cos 180 Degrees The value of cos 180° is given as -1. We can find the value of cos 180 • Using Unit Circle • Using Trigonometric Functions Cos 180 Degrees Using Unit Circle To find the value of cos 180 degrees using the unit circle: • Rotate ‘r’ anticlockwise to form 180° angle with the positive x-axis. • The cos of 180 degrees equals the x-coordinate(-1) of the point of intersection (-1, 0) of unit circle and r. Hence the value of cos 180° = x = -1 Cos 180° in Terms of Trigonometric Functions Using • ±√(1-sin²(180°)) • ± 1/√(1 + tan²(180°)) • ± cot 180°/√(1 + cot²(180°)) • ±√(cosec²(180°) - 1)/cosec 180° • 1/sec 180° Note: Since 180° lies on the negative x-axis, the fin...

Using the above proved results we will prove all six trigonometrical ratios of (180° - θ). sin (180° - θ) = sin (90° + 90° - θ) = sin [90° + (90° - θ)] = cos (90° - θ), [since sin (90° + θ) = cos θ] Therefore, sin (180° - θ) = sin θ , [since cos (90° - θ) = sin θ] cos (180° - θ) = cos (90° + 90° - θ) = cos [90° + (90° - θ)] = - sin (90° - θ), [since cos (90° + θ) = -sin θ] Therefore, cos (180° - θ) = - cos θ , [since sin (90° - θ) = cos θ] tan (180° - θ) = cos (90° + 90° - θ) = tan [90° + (90° - θ)] = - cot (90° - θ), [since tan (90° + θ) = -cot θ] Therefore, tan (180° - θ) = - tan θ , [since cot (90° - θ) = tan θ] csc (180° - θ) = \(\frac\) 2. Find the value of tan 120°. Solution: tan 120° = tan (180 - 60)° = - tan 60°; since we know, tan (180° - θ) = - tan θ = - √3 ● Trigonometric Functions • • • Reciprocal Relations of Trigonometric Ratios • • • • • • • • Trig Ratio Problems • Proving Trigonometric Ratios • • • • • • • • • • • • • • Trigonometrical Ratios of (- θ) • • • Trigonometrical Ratios of (180° + θ) • Trigonometrical Ratios of (180° - θ) • Trigonometrical Ratios of (270° + θ) • T • Trigonometrical Ratios of (360° + θ) • • • • • Trigonometric Functions of any Angles • • 11 and 12 Grade Math From Trigonometrical Ratios of (180° - θ) to HOME PAGE

Value of Cos 180 The value of cos 180 is equal to -1. Trigonometry is the study of measurements of triangles which deals with the length, height and angles of the triangle. The trigonometric functions have an enormous application in the real world. In various fields like engineering, architecture, satellite navigation, medical imaging and the development of sound waves etc. The functions of trigonometry are widely used by engineers, architects, astronauts to calculate the various measurements that undergo the triangular properties. In some applications, it uses the wave pattern of trigonometric functions to produce the sound and light waves. For the creation of computer music, it uses the wave pattern of sine and What is the Value of Cos Pi (180°)? Value of Cos 180 Degree (π) is -1 How to derive the value of Cos 180 Degrees? The value of cos 180 degrees or the value of cos pi can be represented in terms of different angles like 0°, 90°and 270°. Consider the unit circle in which the Cartesian plane is divided into four quadrants. To find the value of cos 180 degrees from the Cartesian plane, the value 180 degree takes place in the second quadrant. As the cosine values in the second quadrant always take a negative value. From the value of cos 0, we will obtain the value of cos 180°. We know that the exact value of cos 0 degrees is 1 So, cos 180 degree is -(cos 0) which is equal to -(1) Therefore, the value of cos 180 degrees = -1 It is also represented in terms of radi...

Using the above proved results we will prove all six trigonometrical ratios of (180° - θ). sin (180° - θ) = sin (90° + 90° - θ) = sin [90° + (90° - θ)] = cos (90° - θ), [since sin (90° + θ) = cos θ] Therefore, sin (180° - θ) = sin θ , [since cos (90° - θ) = sin θ] cos (180° - θ) = cos (90° + 90° - θ) = cos [90° + (90° - θ)] = - sin (90° - θ), [since cos (90° + θ) = -sin θ] Therefore, cos (180° - θ) = - cos θ , [since sin (90° - θ) = cos θ] tan (180° - θ) = cos (90° + 90° - θ) = tan [90° + (90° - θ)] = - cot (90° - θ), [since tan (90° + θ) = -cot θ] Therefore, tan (180° - θ) = - tan θ , [since cot (90° - θ) = tan θ] csc (180° - θ) = \(\frac\) 2. Find the value of tan 120°. Solution: tan 120° = tan (180 - 60)° = - tan 60°; since we know, tan (180° - θ) = - tan θ = - √3 ● Trigonometric Functions • • • Reciprocal Relations of Trigonometric Ratios • • • • • • • • Trig Ratio Problems • Proving Trigonometric Ratios • • • • • • • • • • • • • • Trigonometrical Ratios of (- θ) • • • Trigonometrical Ratios of (180° + θ) • Trigonometrical Ratios of (180° - θ) • Trigonometrical Ratios of (270° + θ) • T • Trigonometrical Ratios of (360° + θ) • • • • • Trigonometric Functions of any Angles • • 11 and 12 Grade Math From Trigonometrical Ratios of (180° - θ) to HOME PAGE

Value of Cos 180 The value of cos 180 is equal to -1. Trigonometry is the study of measurements of triangles which deals with the length, height and angles of the triangle. The trigonometric functions have an enormous application in the real world. In various fields like engineering, architecture, satellite navigation, medical imaging and the development of sound waves etc. The functions of trigonometry are widely used by engineers, architects, astronauts to calculate the various measurements that undergo the triangular properties. In some applications, it uses the wave pattern of trigonometric functions to produce the sound and light waves. For the creation of computer music, it uses the wave pattern of sine and What is the Value of Cos Pi (180°)? Value of Cos 180 Degree (π) is -1 How to derive the value of Cos 180 Degrees? The value of cos 180 degrees or the value of cos pi can be represented in terms of different angles like 0°, 90°and 270°. Consider the unit circle in which the Cartesian plane is divided into four quadrants. To find the value of cos 180 degrees from the Cartesian plane, the value 180 degree takes place in the second quadrant. As the cosine values in the second quadrant always take a negative value. From the value of cos 0, we will obtain the value of cos 180°. We know that the exact value of cos 0 degrees is 1 So, cos 180 degree is -(cos 0) which is equal to -(1) Therefore, the value of cos 180 degrees = -1 It is also represented in terms of radi...

Cos 180 Degrees The value of cos 180 degrees is -1. Cos 180 degrees in radians is written as cos (180°×π/180°), i.e., cos (π) or cos (3.141592. . .). In this article, we will discuss the methods to find the value of cos 180 degrees with examples. • Cos 180°: -1 • Cos (-180 degrees): -1 • Cos 180° in radians: cos (π) or cos (3.1415926 . . .) What is the Value of Cos 180 Degrees? The value of cos 180 degreesis -1. Cos 180 degrees can also be expressed using the equivalent of the given We know, using ⇒ 180 degrees = 180°× (π/180°) rad = π or 3.1415 . . . ∴ cos 180° = cos(3.1415) = -1 Explanation: For cos 180 degrees, the angle 180° lies on the negative x-axis. Thus cos 180° value = -1 Since the cosine function is a ⇒ cos 180° = cos 540° = cos 900°, and so on. Note: Since, cosine is an Methods to Find Value of Cos 180 Degrees The value of cos 180° is given as -1. We can find the value of cos 180 • Using Unit Circle • Using Trigonometric Functions Cos 180 Degrees Using Unit Circle To find the value of cos 180 degrees using the unit circle: • Rotate ‘r’ anticlockwise to form 180° angle with the positive x-axis. • The cos of 180 degrees equals the x-coordinate(-1) of the point of intersection (-1, 0) of unit circle and r. Hence the value of cos 180° = x = -1 Cos 180° in Terms of Trigonometric Functions Using • ±√(1-sin²(180°)) • ± 1/√(1 + tan²(180°)) • ± cot 180°/√(1 + cot²(180°)) • ±√(cosec²(180°) - 1)/cosec 180° • 1/sec 180° Note: Since 180° lies on the negative x-axis, the fin...

Value of Cos 180 The value of cos 180 is equal to -1. Trigonometry is the study of measurements of triangles which deals with the length, height and angles of the triangle. The trigonometric functions have an enormous application in the real world. In various fields like engineering, architecture, satellite navigation, medical imaging and the development of sound waves etc. The functions of trigonometry are widely used by engineers, architects, astronauts to calculate the various measurements that undergo the triangular properties. In some applications, it uses the wave pattern of trigonometric functions to produce the sound and light waves. For the creation of computer music, it uses the wave pattern of sine and What is the Value of Cos Pi (180°)? Value of Cos 180 Degree (π) is -1 How to derive the value of Cos 180 Degrees? The value of cos 180 degrees or the value of cos pi can be represented in terms of different angles like 0°, 90°and 270°. Consider the unit circle in which the Cartesian plane is divided into four quadrants. To find the value of cos 180 degrees from the Cartesian plane, the value 180 degree takes place in the second quadrant. As the cosine values in the second quadrant always take a negative value. From the value of cos 0, we will obtain the value of cos 180°. We know that the exact value of cos 0 degrees is 1 So, cos 180 degree is -(cos 0) which is equal to -(1) Therefore, the value of cos 180 degrees = -1 It is also represented in terms of radi...