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

3. Unit Circle

Trigonometric Functions on the Unit Circle

Trigonometry

3. Unit Circle

Trigonometric Functions on the Unit Circle

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1:33 minutes

Problem 22

Textbook Question

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.sin 45°

Verified step by step guidance

Recall the cofunction identity for sine: \( \sin(\theta) = \cos(90^\circ - \theta) \).

Identify the given angle: \( \theta = 45^\circ \).

Substitute \( \theta = 45^\circ \) into the cofunction identity: \( \sin(45^\circ) = \cos(90^\circ - 45^\circ) \).

Simplify the expression inside the cosine function: \( 90^\circ - 45^\circ = 45^\circ \).

Conclude that \( \sin(45^\circ) = \cos(45^\circ) \).

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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 acute angles, the sine of an angle is equal to the cosine of its complement, and vice versa. For example, sin(θ) = cos(90° - θ). Understanding these identities is crucial for rewriting trigonometric functions in terms of their cofunctions.

Acute Angles

Acute angles are angles that measure less than 90 degrees. In trigonometry, the properties and values of trigonometric functions are often defined specifically for acute angles, as they yield positive values. Recognizing that the question specifies acute angles helps in applying the correct identities and understanding the context of the functions involved.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, are fundamental in relating angles to side lengths in right triangles. Each function has specific values based on the angle's measure. For instance, sin(45°) corresponds to the ratio of the opposite side to the hypotenuse in a right triangle, which is essential for evaluating and rewriting functions in terms of their cofunctions.