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 5.28

Textbook Question

Write each function value in terms of the cofunction of a complementary angle.
tan 174° 03'

Verified step by step guidance

Recognize that the cofunction identity for tangent is: \( \tan(\theta) = \cot(90^\circ - \theta) \).

Convert the given angle from degrees and minutes to a decimal degree: \( 174^\circ 03' = 174 + \frac{3}{60} \).

Calculate the complementary angle: \( 90^\circ - (174^\circ + \frac{3}{60}) \).

Use the cofunction identity to express \( \tan(174^\circ 03') \) in terms of cotangent: \( \tan(174^\circ 03') = \cot(90^\circ - (174^\circ + \frac{3}{60})) \).

Simplify the expression to find the cofunction value.

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) and tan(θ) = cot(90° - θ). 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. In trigonometry, this concept is essential for applying cofunction identities. For instance, if you have an angle of 30°, its complement is 60°. Recognizing complementary angles allows for the transformation of trigonometric functions into their cofunction forms, facilitating easier calculations.

Angle Measurement in Degrees and Minutes

In trigonometry, angles can be measured in degrees and minutes, where 1 degree equals 60 minutes. This notation is important for precise angle representation, especially in problems involving angles greater than 90 degrees or less than 0 degrees. Understanding how to convert between degrees and minutes is necessary for accurately interpreting and solving trigonometric problems involving specific angle measures.