Trig Equation Algebra

Question

how would i solve

150=(11.538^2/cos(x)) (sin(2x))

for x in degrees

Answer 1

Use the identity sin(2x) = 2sin(x)cos(x)

Also, remember that sin^-1(0.5633784027) has 2 answers, one in quadrant 1 and one in quadrant 2. To find the answer in quadrant 2, subtract the "quadrant 1" answer from 180°.

If you go to desmos, switch to "degrees" then graph y = 150 and y = [11.538^2/cos(x)](sin(2x) then you can see where these two intersect and verify your answers.