Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

6. Trigonometric Identities and More Equations

Sum and Difference Identities

Trigonometry

6. Trigonometric Identities and More Equations

Sum and Difference Identities

Previous problemNext problem

Problem 5.26

Textbook Question

Write each function value in terms of the cofunction of a complementary angle.
cot (9π/10)

Verified step by step guidance

Recognize that cotangent is the cofunction of tangent, and use the identity: \( \cot(\theta) = \tan(\frac{\pi}{2} - \theta) \).

Identify the given angle \( \theta = \frac{9\pi}{10} \).

Find the complementary angle by calculating \( \frac{\pi}{2} - \frac{9\pi}{10} \).

Simplify the expression for the complementary angle.

Express \( \cot(\frac{9\pi}{10}) \) as \( \tan(\text{complementary angle}) \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Cofunction Identities

Cofunction identities relate the trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement, and vice versa. This means that for any angle θ, sin(θ) = cos(90° - θ) or sin(θ) = cos(π/2 - θ) in radians. Understanding these identities is crucial for rewriting trigonometric functions in terms of their cofunctions.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees (or π/2 radians). In trigonometry, if you have an angle θ, its complement is given by (90° - θ) or (π/2 - θ). Recognizing complementary angles is essential for applying cofunction identities effectively, as it allows for the transformation of trigonometric expressions.

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function, defined as cot(θ) = 1/tan(θ) = cos(θ)/sin(θ). It is important to understand how cotangent relates to other trigonometric functions, especially when using cofunction identities. For example, cot(θ) can be expressed in terms of the sine and cosine of complementary angles, which aids in rewriting cot(9π/10) in the context of the problem.