Question

Find all solutions if 0° ≤ θ < 360°. When necessary, round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.)
5 cos^2 4θ + 5 sin 4θ = 4
I understand as much as
5(1-sin^24θ)+5sin4θ=4
5-5sin^24θ+5sin4θ=4
-5sin^24θ+5sin4θ+1=0
5sin^24θ-5sin4θ-1=0
quadratic formula:
gets me 5(+/-) sqrt(45) /10 and after that i arcsin but it doesn't give me desired answers.

Answer 1

remember the input is 4x, they want solutions for "x"
\[\sin(4x) = \frac{5 \pm \sqrt{45}}{10}\]
\[x = \frac{\sin^{-1} (\frac{5 \pm \sqrt{45}}{10})}{4}\]

Answer 2

also arc sin yields 2 answers within domain [0,360]
there will be total of 4 solutions

Answer 3

oops nevermind, only 2
the 5+sqrt45 is greater than 10 so arc sin of ratio greater than 1 is impossible

Answer 4

I attached a file as an example of the problem of exactly where I got lost. In the video it stated -.366 somehow turned into 201.5 or 338.5 and quoted "because of sin" which was why I attempted arcsin but the results differ heavily.

Answer 5

oh ok
http://www.wolframalpha.com/input/?i=arcsin%28-.366%29
this is result of arc sin --> look where it gives answer in degrees (-21.5)
-21.5 = 360 -21.5 = 338.5 degrees