## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 2 - Test - Page 97: 7

#### Answer

$\sin(270^{o})=-1$ $\cos(270^{o})= 0$ $\tan(270^{o})$ is not defined $\csc(270^{o})=-1$ $\sec(270^{o})$ is not defined $\cot(270^{o})=0$

#### Work Step by Step

Reference Angle $\theta^{\prime}$ for $\theta$ in $(0^{\mathrm{o}},\ 360^{\mathrm{o}})$ $\left[\begin{array}{lllll} Quadrant: & I & II & III & IV\\ \theta' & \theta & 180^{o}-\theta & \theta-180^{o} & 360^{o}-\theta \end{array}\right]$ $990^{o}$ is coterminal with the angle $990^{o} -2\cdot 360^{o}=990^{o} -720^{o}=270^{o}$ for which the reference angle is $\theta^{\prime}=\theta-180^{o}=270^{o}-180^{o}=90^{o}$ At $90^{o}$ ,tan and sec are not defined, cos and cot are 0 sin and csc are 1. So $\sin(270^{o})=-1$ $\cos(270^{o})= 0$ $\tan(270^{o})$ is not defined $\csc(270^{o})=-1$ $\sec(270^{o})$ is not defined $\cot(270^{o})=0$

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