Question

Evaluate cot870°. 1. - sqrt3 2. -1/sqrt3 3. 1/sqrt3 4. sqrt3

Answer 1

ANSWER

$-\sqrt{3}$

EXPLANATION

The given angle is 870°.

870°-360°-360°=150°

This means that:

870° is coterminal with 150°, hence its terminal side is in the second quadrant.

It makes an acute angle of 30° with the x-axis.

Note that cotangent is negative in the second quadrant,

Hence,

$\cot(870 \degree) = \cot(150 \degree) = - \cot(30 \degree) = - \frac{1}{ \tan(30 \degree) } = - \sqrt{3}$

The first option is correct.