/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 44 Find the exact value of each tri... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Find the exact value of each trigonometric function. Do not use a calculator. $$\cot \frac{5 \pi}{4}$$

Short Answer

Expert verified
The exact value of \( \cot \frac{5 \pi}{4} \) is 1.

Step by step solution

01

Convert Radians to Degrees

Convert the measured in radians angle \(\frac{5\pi}{4}\) to degrees: \(\frac{5\pi}{4} \times \frac{180}{\pi}\) = 225 degrees. Think of the unit circle, this angle is in the third quadrant.
02

Find Sin and Cos Values

Recall that in the unit circle, a 45 degrees angle in the third quadrant has the sine and cosine values as -1/√2 or -√2/2.
03

Calculate Cotangent

The trigonometric function cotangent is the reciprocal of the tangent function, and the tangent function is the ratio of sine to cosine. So, cotangent = cos/sin = -√2/2/ (-√2/2) = 1

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