hi Skylor,

From the look of this question, you are expected to do this without a calculator.

Set adjacent = 40 and hypotenuse = 41 .  Then work out the 'opposite' using Pythagoras.

(As the angle is not acute you may wonder if this is valid but, at this stage you may treat it as if it is acute)

That means you can write down a value for sin θ.

But now you must adjust your answer (+ or -) according to which quadrant this angle lies in.

After that you can get the angles you want with

sin2θ = 2sinθcosθ

cos2θ= (cosθ)^2 - (sinθ)^2

tan 2θ = 2tanθ/( 1 - [tanθ]^2 )  or  sin2θ/cos2θ
 
Of course you can also check your answers using a calculator.

Bob

given cos θ = 40/41, θ lies in quadrant IV

find sin 2θ, cos 2θ, and tan 2θ