Question

Find the values of the trigonometric function for the following: $cot(-\frac{15\pi }{4})$

Answer 1

Given, $cot\left(-\frac{15\pi}{4}\right)$

first of all we have to resolve $\left(-\frac{15\pi}{4}\right)$

$\left(-\frac{16\pi-\pi}{4}\right)$

$\left(-\frac{16\pi}{4}+\frac{\pi}{4}\right)$

$\left(-4\pi+\frac{\pi}{4}\right)$

now, $cot\left(-4\pi+\frac{\pi}{4}\right)=cot\left(2\pi(-2)+\frac{\pi}{4}\right)$

we know, cotx = cot(2nπ + x), where n is integral number.

so, $cot\left(2\pi(-2)+\frac{\pi}{4}\right)=cot\frac{\pi}{4}=1$

hence, $cot\left(-\frac{15\pi}{4}\right)$ = 1