Use graphing utility to approximate the solutions of the equation in the interval [0, 2𝜋). ( Round your answers to four decimal places.) sin x + 𝜋 2 + cos2 x = 0

Answer 1

I believe you meant the first term to be

sin x + pi/2 which is equal to cosine x

Make this substitution and you get

cos(x) +cos^2(x)=0

now factor out cos(x) and you have

cosx( 1+ cosx)= 0

The 2 solutions are cos(x)= 0 which is at pi/2 and 3pi/2

and cos(x)=-1 which occurs at pi so the solutions are

x=pi/2, pi and 3pi/2