If cos(θ) = -0.5 and angle θ is in quadrant 2, what are the values of sin(θ) and tan(θ)?

Answer 1

Look up a figure of a 30-60-90 right triangle and you'll see that cos(60°) = 1/2, sin(60°) = (√3)/2, and tan(60°) = √3.

In Quadrant II, where the cosine is negative, the angle (θ) with a reference angle of 60° is 180° - 60° = 120°, so cos(120°) = -1/2.

The sine is positive in QII, so sin(120°) = (√3)/2.

The tangent is negative in QII, so tan(120°) = -√3.

There, you should now be happy! ;-)