Question

Suppose that cos(θ) = 1/3 and cos(2θ) = -2/√3. Find the value of sin(-2θ).

a) -2/3
b) 2/3
c) √3/2
d) -√3/2

Answer 1

To find the value of sin(-2θ), we can use the double-angle identity for sine and substitute the given values. The value of sin(-2θ) is √3/2.

Step-by-step explanation:

To find the value of sin(-2θ), we can use the double-angle identity for sine. The double-angle identity for sine states that sin(2θ) = 2sin(θ)cos(θ).

Since we already know the value of cos(θ) and cos(2θ), we can substitute them into the double-angle identity to find sin(2θ).

sin(2θ) = 2sin(θ)cos(θ) = 2 * (1/3) * (-2/√3) = -4/√3.

Next, we can use the identity sin(-x) = -sin(x) to find sin(-2θ).

sin(-2θ) = -sin(2θ) = -(-4/√3) = 4/√3 = (√3/3) * (4/√3) = √3 * (4/3) = √3/2.