Question

How do you find sin2x if sinx = -3/5 and x is in quadrant 3?

Answer 1

find sin 2x, knowing `sin x = -3/5`

Ans: 0.96

Explanation:

There are 2 ways:
1. First way.
Calculator gives --> `sin x = -3/5 = - 0.60` --> x = -36.87 deg
and x = 180 + 36.87 = 216.87 (Quadrant III)
Then, 2x = 2(216.87) = 433.74 = (73.74 + 360) deg -->
--> sin 2x = sin 73.74 = 0.96

1. Second way
   sin x = -0.6 --> `sin^2 x = 0.36` --> `cos^2 x = 1 - 0.36 = 0.64`-->
   --> `cos x = +- 0.8`. Since x is located in Quadrant III, then,
   `cos x = - 0.8`

sin 2x = 2sinx.cos x = 2(-0.6)(-0.8) = 0.96