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°)

검증된 단계별 안내

Recognize that the expression involves the cosine of a difference: \(\cos(90^\circ - 3.69^\circ)\).

Recall the co-function identity in trigonometry: \(\cos(90^\circ - \theta) = \sin(\theta)\).

Apply this identity to rewrite the expression as \(\sin(3.69^\circ)\).

Use a calculator to find the sine of \(3.69^\circ\). Make sure your calculator is set to degree mode.

Round the result to six decimal places as requested.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Complementary Angle Identity

The complementary angle identity states that cos(90° - θ) = sin(θ). This relationship allows simplification of trigonometric expressions by converting cosine of a complementary angle into sine, which can be easier to evaluate or interpret.

Using a Calculator for Trigonometric Values

Calculators can compute trigonometric functions like sine and cosine, but the angle mode (degrees or radians) must be set correctly. For angles given in degrees, ensure the calculator is in degree mode to get accurate results.

Rounding and Decimal Precision

When approximating values, it is important to round the result to the specified number of decimal places. Here, answers should be rounded to six decimal places to maintain consistency and precision in reporting the value.

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°)