Question

Solve the equation on the interval 0≤θ<2π:
2cos²θ-1 = 0

Answer 1

start with
\[\cos^2(x)=\frac{1}{2}\]

Answer 2

take the square root, don't forget the \(\pm\)

Answer 3

you get
\[\cos(x)=\pm\frac{1}{\sqrt{2}}\] which you might recognize better as
\[\cos(x)=\pm\frac{\sqrt{2}}{2}\]

Answer 4

then see if you know some angles \(x\) where
\[\cos(x)=\frac{\sqrt{2}}{2}\] and also where
\[\cos(x)=-\frac{\sqrt{2}}{2}\]

Answer 5

Thank you!

Answer 6

yw
you good from there?