Chapter 3 - Test - Page 132: 16

We can find the domain of $sin ~\theta$: domain: $-\infty \lt \theta \lt \infty$ We can find the domain of $cos ~\theta$: domain: $-\infty \lt \theta \lt \infty$ We can find the domain of $tan ~\theta$: domain: $\theta \neq \frac{\pi}{2}+\pi~n$, for any integer $n$ We can find the domain of $csc ~\theta$: domain: $\theta \neq \pi~n$, for any integer $n$ We can find the domain of $sec ~\theta$: domain: $\theta \neq \frac{\pi}{2}+\pi~n$, for any integer $n$ We can find the domain of $cot ~\theta$: domain: $\theta \neq \pi~n$, for any integer $n$

We can find the domain of $sin ~\theta$: $sin~\theta = \frac{x}{r}$ Since $r$ is always positive, $sin ~\theta$ is defined for all real numbers. domain: $-\infty \lt \theta \lt \infty$ We can find the domain of $cos ~\theta$: $cos~\theta = \frac{y}{r}$ Since $r$ is always positive, $cos ~\theta$ is defined for all real numbers. domain: $-\infty \lt \theta \lt \infty$ We can find the domain of $tan ~\theta$: $tan~\theta = \frac{sin~\theta}{cos~\theta}$ $tan ~\theta$ is undefined when $cos~\theta = 0$ $tan ~\theta$ is undefined when $\theta = \frac{\pi}{2}+\pi~n$, for any integer $n$ domain: $\theta \neq \frac{\pi}{2}+\pi~n$, for any integer $n$ We can find the domain of $csc ~\theta$: $csc~\theta = \frac{1}{sin~\theta}$ $csc ~\theta$ is undefined when $sin~\theta = 0$ $csc ~\theta$ is undefined when $\theta = \pi~n$, for any integer $n$ domain: $\theta \neq \pi~n$, for any integer $n$ We can find the domain of $sec ~\theta$: $sec~\theta = \frac{1}{cos~\theta}$ $sec ~\theta$ is undefined when $cos~\theta = 0$ $sec ~\theta$ is undefined when $\theta = \frac{\pi}{2}+\pi~n$, for any integer $n$ domain: $\theta \neq \frac{\pi}{2}+\pi~n$, for any integer $n$ We can find the domain of $cot ~\theta$: $cot~\theta = \frac{cos~\theta}{sin~\theta}$ $cot ~\theta$ is undefined when $sin~\theta = 0$ $cot ~\theta$ is undefined when $\theta = \pi~n$, for any integer $n$ domain: $\theta \neq \pi~n$, for any integer $n$