Answer
The value of the trigonometric function $\cot \left( -\frac{\pi }{4}+17\pi \right)$ is $-1$.
Work Step by Step
Consider the trigonometric function, $\cot \left( -\frac{\pi }{4}+17\pi \right)$
Use the property $\cot \left( t+n\pi \right)=\cot t$.
Here, the value of $t$ is $-\frac{\pi }{4}$ and the value of $n$ is $17$.
$\cot \left( -\frac{\pi }{4}+17\pi \right)=\cot \left( -\frac{\pi }{4} \right)$
Use the property $\cot \left( -t \right)=-\cot t$.
$\cot \left( -\frac{\pi }{4}+17\pi \right)=-\cot \frac{\pi }{4}$
The value of $\cot \frac{\pi }{4}$ is $1$.
So,
$\cot \left( -\frac{\pi }{4}+17\pi \right)=-1$
Therefore, the value of the trigonometric function $\cot \left( -\frac{\pi }{4}+17\pi \right)$ is $-1$.
