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marissa [1.9K]
3 years ago
10

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

Mathematics
1 answer:
ivolga24 [154]3 years ago
3 0

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.

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