Chapter 4.2, Problem 86E

(a)

To determine

Find the value of the Trigonometric function $\cos (\text{π}\text{-}\text{t})$ when $\cos t=-\frac{1}{7}$

Answer to Problem 86E

  $\frac{1}{7}$

Explanation of Solution

Given: The Trigonometric Function $\cos t=-\frac{1}{7}$

Concept Used:

We know that $\cos (\text{π}\text{-}\text{t})$ is in the 2^nd quadrant and in 2^nd quadrant cosine function is negative.

Calculation:

$\begin{array}{l}\cos (\text{π}\text{-}\text{t})=-\cos \text{t}=-(-\frac{1}{7})=\frac{1}{7}\\ \cos (\text{π}\text{-}\text{t})=\frac{1}{7}\end{array}$

Thus, the value of the function is $\cos (\text{π}\text{-}\text{t})=\frac{1}{7}$

(b)

To determine

Find the value of the Trigonometric function $\cos (\text{π}+\text{t})$ when $\cos t=-\frac{1}{7}$

Answer to Problem 86E

  $\frac{1}{7}$

Explanation of Solution

Given: The Trigonometric Function $\cos t=-\frac{1}{7}$

Concept Used:

We know that $\cos (\text{π}+\text{t})$ is in the 3^rd quadrant and in 3^rd quadrant cosine function is negative.

Calculation:

$\begin{array}{l}\cos (\text{π}+\text{t})=-\cos \text{t}=-(-\frac{1}{7})=\frac{1}{7}\\ \cos (\text{π}+\text{t})=\frac{1}{7}\end{array}$

Thus, the value of the function is $\cos (\text{π}+\text{t})=\frac{1}{7}$