Answer:
30 degrees
Step-by-step explanation:
360 - 210 = 150 degrees
cot -210 = cot 150
= - cot 30
= - 1 / tan 30.
So 30 degrees can be used here.
The cotangent period is 180°.
Therefore
[tex]\cot(-210^o)=\cot(-210^o+180^o)=\cot(-30^o)[/tex]
Cotangent is an odd function. Hence:
[tex]\cot(-x)=-\cot(x)[/tex]
Therefore
[tex]\cot(-30^o)=-\cos30^o[/tex]
[tex]\cot30^o=\sqrt3[/tex]
Answer:
[tex]\boxed{\cot(-210^o)=-\sqrt3}\to\text{Use}\ 30^o[/tex]
