Question

e.g. tan 315 = -1, does that work in our equation ??

Yes, thank you again Reiny!

My next question is to find sin theta and cos theta.

cos 2theta = 1/3 and pi less than or equal to 2theta less than or equal to 2pi

I hope Im not overburdening you with question:/

Answer 1

<<I hope Im not overburdening you with question:/>>

lol, I love trig and do these kind of questions for recreation.

for this one you will need to know

1. sin2A = 2sinAcosA, and
2. cos2A = cos^2 A - sin^2 A
or 2cos^2 A -1
or 1 - 2sin^2 A

I will do the first, you do the second


cos2A = 1-2sin^2A
1/3 = 1 - 2sin^2 A
2 sin^2 A = 1 - 1/3
sin^2 A = 1/3
sinA = ±1/√3 (I used A instead of theta)

Can we use both ± ?
2theta is in either I or IV
then theta is in either I or II, but the sine in both of these is positive, so

sinA = +1/√3 only.

you try the second one.