Chapter 5.3, Problem 24E

To determine

To find: The values of six trigonometric functions for ${315}^{\circ }$ , using the unit circle.

Answer to Problem 24E

  $\begin{array}{l}\sin {315}^{\circ }=\frac{-\sqrt{2}}{2},\csc {315}^{\circ }=-\sqrt{2}\\ \cos {315}^{\circ }=\frac{\sqrt{2}}{2},\sec {315}^{\circ }=\sqrt{2}\\ \tan {315}^{\circ }=-1,\cot {315}^{\circ }=-1\end{array}$

Explanation of Solution

Given information: ${315}^{\circ }$

Calculation:

  

  $\begin{array}{l}\sin {315}^{\circ }=\frac{-\sqrt{2}}{2}\\ \csc {315}^{\circ }=\frac{1}{\frac{-\sqrt{2}}{2}}=\frac{-2}{\sqrt{2}}=-\sqrt{2}\\ \cos {315}^{\circ }=\frac{\sqrt{2}}{2}\\ \sec {315}^{\circ }=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\\ \tan {315}^{\circ }=\frac{\sin }{\cos }=\frac{\frac{-\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=-1\\ \cot {315}^{\circ }=\frac{1}{\tan }=\frac{1}{-1}=-1\end{array}$