Find all solutions of \(cos^2(\theta)=\frac{1}{2}\) on the interval
\(0 <= \theta < 2\pi\)
I know that \(cos(\theta)=\frac{1}{2}\) on the interval at pi/3 and 5pi/3 but how do I deal with the squared cosine introducing more solutions?
+129840 cos^2 θ = 1/2
Take.....positive and negative square root
cos θ = ± 1 / √2
First
cos θ = + 1 / √2 and this occurs at pi/4 and at 7pi/4 [45° and 315° ]
Second
cos θ = - 1 / √2 and this occurs at 3pi/4 and at 5pi/4 [135° and 225°]
Here's the graph [in degrees ] : https://www.desmos.com/calculator/kr6lmsgjlc
