please help with these

Question

a) Solve 

for all solutions 

t = 

b) Solve  for all solutions 

c) Solve 

 for all solutions.

Your initial angle should be between 0 and  (not including  , and your initial angles should go from least to greatest. Consider  to have an initial angle of 0). Use  as your multiplier.

Answer 1

Need to use your double angle formula to get 8( cos^2(t) -sin^2(t)= 8 sin^2(t) +3

8cos^2(t) -8sin^2(t) =8sin^2(t) +3 Use the identity cos^2(t) = 1-sin^2(t)

8(1-sin^2(t)) -8sin^2(t) =8sin^2(t) +3\

8- 8sin^2(t) -8sin^2(t) = 8sin^2(t) +3

8 -16sin^2(t) =8sin^2(t) +3

24 sin^2(t) = 5 sin^2(t) =5/24 sin(t) = +/- sqroot (5/24) Take the inverse sin to get the angles +/- 27.16 degrees You will have angles in all 4 quadrants 27.16, (180-27.16) 180+27.16 and -27.16

For the second problem use your double angle formula to change 8sin(2w) to 8( 2sin(w)cos(w) = 16sin(w)cos(w). I will leave it to you to solve from here

For problem 3 Factor the expression to (2sinx +1)(sinx+1) =0 so sinx = -1/2 and -1 I will leave it to you to find these angles