Question

What is the exact value of sin(2 theta) if cos (theta)=3/5 and (theta) is in quadrent 4?

12/25
24/25
-12/25
-7/25
-24/25

Answer 1

cos(theta) = 3/5

Use your calculator:

cos-1(3/5) = theta = 53.13 degrees
This is the value that your calculator gives, and it is in quadrant; To find the value theta corresponding to quadrant 4, notice the symmetry in a graph of cos x, which is that cos(x), cos(x) = cos(360 - x); 306.87 = theta in quadrant 4
quadrant 1 (0 - 90 degrees)
quadrant 2 (90 - 180 degrees)
quadrant 3 (180 - 270 degrees)
quadrant 4 (270 - 360 degrees)

Use your calculator to calculator sin(2*306.87)

Answer 2

-24/25