# Math Help - Use the identity cos^2(theta) + sin^2(theta) = 1

1. ## Use the identity cos^2(theta) + sin^2(theta) = 1

Use the identity cos^2(θ) + sin^2(θ) = 1 to find sin(θ) when cos(θ) = 0.5

Really lost on this. Is it something to do with the identities cos^2(x) = 1/2 + 1/2 cos(2x) and sin^2(x) = 1/2 - 1/2 cos(2x) ?

Please provide a solution with steps.

2. ## Re: Use the identity cos^2(theta) + sin^2(theta) = 1

$\pm \sqrt{1-0.5^2}$

3. ## Re: Use the identity cos^2(theta) + sin^2(theta) = 1

$\cos^2 \theta + \sin^2 \theta = 1$

$(0.5)^2 + \sin^2 \theta = 1$

$\sin^2 \theta = 1 - 0.25$

$\sin \theta = \pm \sqrt{0.75} = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}$