Question

find -cot(pi/4+17pi)

Answer 1

could you clarify? is it pi/(4+17pi) or pi/4 + 17pi

Answer 2

\(\bf -cot\left(\frac{\pi}{4}+17\pi\right)\implies \cfrac{cos\left(\frac{\pi}{4}+17\pi\right)}{-sin\left(\frac{\pi}{4}+17\pi\right)}\implies
\cfrac{cos\left(\frac{\pi}{4}+17\pi\right)}{sin\left[-\left(\frac{\pi}{4}+17\pi\right)\right]}
\\ \quad \\
\cfrac{cos\left(\frac{\pi}{4}+17\pi\right)}{sin\left(17\pi-\frac{\pi}{4}\right)}\implies \cfrac{cos(17\pi)cos\left(\frac{\pi}{4}\right)-sin(17\pi)sin\left(\frac{\pi}{4}\right)}{sin(17\pi)cos\left(\frac{\pi}{4}\right)-cos(17\pi)sin\left(\frac{\pi}{4}\right)}\)

Answer 3

cot(x) = cos(x) / sin(x) is periodic with period pi. thus
-cot(pi/4 + 17pi) = -cot(pi/4) = -cos(pi/4)/sin(pi/4) (look in the unit circle. x=y) = -1