SOLUTION: 4 cos^2 (4θ) + 4 sin (4θ) = 3

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Question 1029080: 4 cos^2 (4θ) + 4 sin (4θ) = 3
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Substitute


Two "u" solutions:



So then,





So,




and




So,




8 solutions
.
.
.




Since cosine can never equal this value, this u solution does not yield a theta solution.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
4cos^2(t) + 4sin(t) = 3
4(1 - sin^2(t)) + 4sin(t) = 3
4sin^2 - 4sin - 1 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=32 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.20710678118655, -0.207106781186548. Here's your graph:

-------------
sin(t) =~ -0.2071
t =~ 192, 348 degs
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