Question 329512
BIG TIP:  Post one question at a time or else no one will reply.

I will do question 6 only.

6. Find the exact value of sin 2 θ given that cos θ = 12/13 and θ is in Quadrant I.


We are in quadrant 1 which means all trig functions are positive.  So, there's no need to worry about signs in this case.

Using a right triangle in the first quadrant, we know that cos(theta) = adj/hyp.
Using the Pythagorean Theorem, we also learn that the missing side is 5. 

sin(theta) = opp/hyp

sin(theta) = 5/13

cos(theta) = adj/hyp

cos(theta) = 12/13

We now plug it into the formula sin(2θ) = 2sin(θ)cos(θ) and simplify.

sin(2θ) = 2(5/13)(12/13)

sin(2θ) = 2(5/13)(12/13)

sin(2θ) = 120/169

CHOICE B