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°)

Key Concepts

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.