Question

How do you solve `2cos^2theta-4costheta-5=0` in the interval `0<=x<=2pi`?

Answer 1

`theta=150.56` deg

Explanation:

`2cos^2theta-4costheta-5=0`. Note that this equation looks like the quadratic equation `2x^2-4x-5=0`. So we will solve using the quadratic formula `x=(-b+- sqrt((b^2-4ac)))/(2a)`
`a=2,b=-4,c=-5`

`costheta=(4+- sqrt(16-4(2)(-5)))/4`

`costheta=(4+-sqrt56)/4`

`costheta=(4+sqrt56)/4` or `costheta=(4-sqrt56)/4`

`theta=cos^-1((4+sqrt56)/4)` or `theta=cos^-1((4-sqrt56)/4)`
`theta=`undefined or `theta=150.56` deg