Question

Which of the following angles can be used to evaluate cot(-210)

Answer 1

30 degrees

Explanation:

360 - 210 = 150 degrees

cot -210 = cot 150

= - cot 30

= - 1 / tan 30.

So 30 degrees can be used here.

Answer 2

The cotangent period is 180°.

Therefore

`\cot(-210^o)=\cot(-210^o+180^o)=\cot(-30^o)`

Cotangent is an odd function. Hence:

`\cot(-x)=-\cot(x)`

Therefore

`\cot(-30^o)=-\cos30^o`

`\cot30^o=\sqrt3`

Answer:

`\boxed{\cot(-210^o)=-\sqrt3}\to\text{Use}\ 30^o`