find all values of theta 0<= theta<=3pi for which sin^2theta=1/2 answer in radians

Question

if anyone can help it would be a huge help, I've been trying to work this out for days

Answer 1

I think you 2pi rather than 3pi.

 

 

Let       x=θ

 

sin²(x) = 1/2

 

 

Square-root both sides of the equation.

 

sin(x) = √(1 / 2)

 

sin(x) = 1 / √2

 

sin(x) = √(2) / 2

 

 

Take the inverse of sin(x).

 

x = sin^-1(√(2) / 2)

 

x = π/4

 

 

Since sine is positive in the 1st and 2nd quadrants, the other angle will be

 

x = π - (π/4)