Suppose θ is an angle in standard position whose terminal side lies in quadrant iii.

  B)  -(√21)/5

Step-by-step 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

___

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.

need more information

step-by-step explanation: