Find the exact value. - sin 150° - cos 150°

Hello!

The easiest way to solve for the value of both angles is to reduce the given angle to an acute angle.

Given that both of the angles are located in the second quadrant (90° < x < 180°), we use these reduction formulas: sin(180° - x) = sin x, and cos(180° - x) = -cos x, when x is equal to 150°.

Notice that cos is negative while sin is positive. In the first quadrant, sine is always positive and while in the fourth quadrant, cosine is always positive while sine is not.

sin(180° - 150) = sin 30 = 1/2 (using the unit circle)

cos(180° - 150) = -cos 30 = -√3/2 (using the unit circle)

Final answers:

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