In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
cot 𝜋/12

검증된 단계별 안내

Recognize that the problem asks for \( \cot \frac{\pi}{12} \), which is the cotangent of \( \frac{\pi}{12} \) radians. Cotangent is the reciprocal of tangent, so \( \cot x = \frac{1}{\tan x} \).

Convert the angle \( \frac{\pi}{12} \) radians to degrees if needed for your calculator. Since \( \pi \) radians equals 180 degrees, \( \frac{\pi}{12} = \frac{180}{12} = 15^\circ \).

Use the calculator to find \( \tan 15^\circ \). Make sure your calculator is set to degree mode if you use degrees, or radian mode if you input the angle in radians.

Calculate the cotangent by taking the reciprocal of the tangent value: \( \cot \frac{\pi}{12} = \frac{1}{\tan \frac{\pi}{12}} \).

Round the result to four decimal places as requested.

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주요 개념

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Understanding the Cotangent Function

Cotangent 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). It is the reciprocal of the tangent function and is used to find angles or side ratios in trigonometry.

Radian Measure and Angle Conversion

Angles in trigonometry can be measured in degrees or radians. The given angle π/12 is in radians, where π radians equal 180 degrees. Understanding how to interpret and convert radians is essential for evaluating trigonometric functions accurately.

Using a Calculator for Trigonometric Values

Calculators can compute trigonometric functions directly in radians or degrees. To find cot(π/12), one typically calculates tan(π/12) first and then takes its reciprocal. Ensuring the calculator is set to the correct mode (radians) is crucial for accurate results.

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.cot 𝜋/12