Question

If sin x = 3/5 with x in the second quadrant, find the value of sin 2x.

a) sin 2x = -24/25
b) sin 2x = -4/5
c) sin 2x = -6/25
d) sin 2x = -3/5

Answer 1

The double-angle formula for sine is used to calculate sin 2x when sin x = 3/5 and x is in the second quadrant. The correct value of sin 2x is found to be -24/25.

Step-by-step explanation:

If sin x = 3/5 and x is in the second quadrant, we can use the double-angle formula for sine to find sin 2x. The double-angle formula states that sin 2x = 2sin x cos x. Knowing that x is in the second quadrant means that the cosine of x is negative because cosine is negative in the second quadrant. First, we find cos x using the Pythagorean identity: cos2 x + sin2 x = 1, which means cos2 x = 1 - sin2 x = 1 - (3/5)2 = 1 - 9/25 = 16/25. So cos x = -√(16/25) = -4/5 (negative because x is in the second quadrant).

Now, we can calculate sin 2x: sin 2x = 2 * (3/5) * (-4/5) = 2 * -12/25 = -24/25.

The correct answer is option a) sin 2x = -24/25.