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.
cot(90°-4.72°)

검증된 단계별 안내

Recall the co-function identity for cotangent: \(\cot(90^\circ - \theta) = \tan(\theta)\).

Apply this identity to the given expression: \(\cot(90^\circ - 4.72^\circ) = \tan(4.72^\circ)\).

Use a calculator to find the value of \(\tan(4.72^\circ)\). Make sure your calculator is set to degree mode.

Calculate the tangent value and round the result to six decimal places.

Write the final answer as the approximate value of \(\cot(90^\circ - 4.72^\circ)\) rounded to six decimal places.

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주요 개념

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

Cotangent and Its Definition

Cotangent (cot) is a trigonometric function defined as the ratio of the adjacent side to the opposite side in a right triangle, or equivalently, cot(θ) = 1/tan(θ). Understanding cotangent helps in evaluating expressions involving cotangent values.

Complementary Angle Identity

The complementary angle identity states that cot(90° - θ) = tan(θ). This identity allows simplification of cotangent expressions involving angles subtracted from 90°, making calculations easier by converting cotangent to tangent.

Using a Calculator for Trigonometric Approximations

Calculators can approximate trigonometric values to a desired decimal precision. After simplifying expressions using identities, input the angle in degrees and use the calculator’s tangent function to find the value, rounding the result to six decimal places as required.

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. cot(90°-4.72°)