Question

Suppose θ is an angle in standard position whose terminal side lies in Quadrant III.

Answer 1

B) -(√21)/5

Explanation:

In quadrant III, both sine and cosine are negative, so the sine will be given by ...

sin = -√(1 -cos^2)

sin(θ) = -√(1 -(-2/5)^2) = -√((25-4)/25) = -√(21)/5

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Comment on choices

You can eliminate the choices with 2 in the denominator, as those all have a magnitude greater than 1. That leaves choices with either a positive or negative sign. If you're paying attention to the signs of the trig functions, you know you want a negative sign, selection B.