Question

Find the value for sin(θ) if the following conditions hold: cos(2 theta) = 3/4 and 270 degrees

Answer 1

sin(θ) = - 0.35355

Explanation:

The second condition is

270 degrees<theta<360 degrees

cos(2*theta) = 3/4

And we know the relation

cos(2*θ)=1-2sin^2(θ)

This means that,

sin^2(θ) = 0.5*(1-cos(2*θ))

sin(θ) = ± √(0.5*(1-cos(2*θ)))

sin(θ) = ± √ (0.125)

sin(θ) = ± 0.35355

But we are in the 4th quadrant.

This means that the sine is negative.

sin(θ) = - 0.35355