SOLUTION: Find the solution of sin2(theta)=cos(theta) if 0 deg. <= (theta) < 180 deg.

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Question 350263: Find the solution of sin2(theta)=cos(theta) if 0 deg. <= (theta) < 180 deg.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the solution of sin2(theta)=cos(theta) if 0 deg. <= (theta) < 180 deg.
If sin2(theta) = sine squared of theta:

sub x for cos(theta)


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=5 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.618033988749895, -1.61803398874989. Here's your graph:

x = -1/2 ± sqrt(5)/2
cos(theta) = -1/2 ± sqrt(5)/2
Use a calculator to find theta.
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