Question

Select the functions that have a value of 0.

sin270
cos90
tan0
csc(-180)
cos(-90)
cot270

Answer 1

cos90° = 0°, tan0° = 0°,cos(-90°) = 0°, cot270° = 0°

Explanation:

Answer 2

cos90° = 0°, tan0° = 0°,

cos(-90°) = 0°, cot270° = 0°

Explanation:

`k\in\mathbb{Z}\\\\\sin x=0\iff x=180^ok\\\\\cos x=0\iff x=90^o+180^ok\\\\\tan x=0\iff x=180^ok\\\\\cot x=0\iff x=90^o+180^ok\\\\\csc x\\eq0\ \text{for}\ x\in\mathbb{R}-\{180^ok\}\\========================\\\\\sin270^o\\eq0\\\\\cos90^o=\cos(90^o+180^o\cdot0)=0\\\\\tan0^o=\tan(180^o\cdot0)=0\\\\\csc(-180^o)\\eq0\\\\\cos(-90^o)=\cos(90^o-180^o)=\cos(90^o+180^o\cdot(-1))=0\\\\\cot270^o=\cot(90^o+180^o)=0`