Question

Double-Angle and Half-Angle Identiies [See Attachment] Question3

Answer 1

Seems to be a q and a theta here; presumably they're the same.

`\sin \theta = - \frac 3 5`

`\cos \theta = + √( 1- \sin^2 \theta) = √(1- 9/25) = \frac 4 5`

I chose the positive cosine because we're (almost) told
`\theta` is in the fourth quadrant.

`\tan \theta = (\sin \theta)/(\cos \theta ) = (-3/5)/(4/5) = - \frac 3 4`

`\tan 2 \theta = (2 \tan \theta)/(1 - \tan^2 \theta) = (-3/2)/(1 - 9/16) = - (24)/(7)`

Choice b