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.

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

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

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

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

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

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

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