Question

Given that the value of x is between 0 and 360 degrees (0 and 360

included), solve for x: cos(x) = -(square root 3)/2*

cos(x) = - square root of 3/2

60 and 120
-30 and 150
150 only
150 and 210

Answer 1

• 150° and 210°
• 0

Explanation:

It is convenient to memorize the trig functions of the "special angles" of 30°, 45°, 60°, as well as the way the signs of trig functions change in the different quadrants. Realizing that the (x, y) coordinates on the unit circle correspond to (cos(θ), sin(θ)) can make it somewhat easier.

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20.

You have memorized that cos(x) = (√3)/2 is true for x = 30°. That is the reference angle for the 2nd-quadrant angle 180° -30° = 150°, and for the 3rd-quadrant angle 180° +30° = 210°.

Cos(x) is negative in the 2nd and 3rd quadrants, so the angles you're looking for are

150° and 210°

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Bonus

You have memorized that sin(π/4) = √2/2, and that cos(3π/4) = -√2/2. The sum of these values is ...

√2/2 + (-√2/2) = 0

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Additional comments

Your calculator can help you with both of these problems.

The coordinates given on the attached unit circle chart are (cos(θ), sin(θ)).