Question

Double-Angle and Half-Angle Identiies [See Attachment] Question 5

Answer 1

Thought I did this one but it was just very similar. Again there's a q and a theta I'm just going to assume are the same.

$\sin \theta = \pm \sqrt{1 - \cos^2 \theta}$

$\sin \theta = + \sqrt{1 - (3/5)^2} = \frac 4 5$

I picked positive because we're in the first quadrant.

$\sin 2 \theta = 2 \sin \theta \cos \theta$

$\sin 2 \theta = 2 (\frac 4 5)(\frac 3 5) = \frac {24}{25}$