Answer: first choice!
sin2Theta= -4rt21/25
cos2Theta = 17/25
Explanation:
Use Double Angle Formulas.
You can find cos2Theta immediately because one of the formulas needs only sin(theta) and that was given.
Cos2Theta =
1 - 2(sinTheta)^2
= 1 - 2(-2/5)^2
= 1 - 2(4/25)
= 1 - 8/25
= 25/25 - 8/25
= 17/25
The only answer with cos2theta=17/25 is the first choice.
Use a simple graph and Pythagorean Theorem to find cos(theta). Then you can use the Double Angle Formula for sin2theta. This would kinda be a double check if you have time. Since the first part of the solution eliminated all choices except the first choice, if you're pressed for time just do cos2theta calculation and pick the first choice.
See image for sin2theta calculation.