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

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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2: minutes

Problem 26

Textbook Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.cos(90°-3.69°)

Verified step by step guidance

Recognize that the expression cos(90° - \theta) can be simplified using the co-function identity: cos(90° - \theta) = sin(\theta).

Substitute \theta = 3.69° into the identity: cos(90° - 3.69°) = sin(3.69°).

Use a calculator to find the sine of 3.69°.

Ensure the calculator is set to degree mode before calculating.

Round the result to six decimal places.

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Key Concepts

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

Complementary Angles

In trigonometry, complementary angles are two angles whose sum is 90 degrees. This concept is crucial for simplifying expressions involving trigonometric functions, as it allows the use of co-function identities. For example, the cosine of an angle can be expressed as the sine of its complement, which is useful in this problem.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables. The co-function identity states that cos(90° - θ) = sin(θ). This identity is essential for simplifying the expression cos(90° - 3.69°) before using a calculator to find the value.

Calculator Precision

Calculator precision refers to the number of decimal places to which a calculator can provide an answer. In this question, the requirement to give answers to six decimal places emphasizes the importance of accuracy in calculations. Understanding how to set a calculator for the desired precision is vital for obtaining the correct result.