Question

Find the exact value. cos150°

Answer 1

-√3/2

Explanation:

Cos 150° can also be rewritten as shown;

Cos 150° = cos(90°+60°)

According to trigonometry identity

Cos(A+B) = cosAcosB - sinAsinB

Therefore;

Cos(90°+60°) = cos90cos60-sin90sin60

Cos(90°+60°) = 0(1/2) - 1(√3/2)

Cos(90°+60°) = 0-√3/2

Cos(90°+60°) = -√3/2

Cos 150° = -√3/2

Answer 2

`\cos(150 \degree) = - ( √(3) )/(2)`

EXPLANATION

We want to find the exact value of cos(150°).

150° makes an angle of 30° with the positive direction of the x-axis and it is also in the second quadrant.

The cosine ratio is negative in the second quadrant.

Using the unit circle,

`\cos(150 \degree) = - \cos(30 \degree) = - ( √(3) )/(2)`