Question

How are the values for theta derived using the quadratic formula?

How are these solutions derived using the quadratic formula?

Answer 1

Answer is `55.96^@` and `153.27^@`

Explanation:

`1.5(2cos^2theta-1)+costheta=0` can be written as

`3cos^2theta-1.5+costheta=0`

or `6cos^2theta+2costheta-3=0`

As it is a quadratic equation, with `costheta` as variable, we solve for it using quadratic formula and

`costheta=(-2+-sqrt(2^2-4*6*(-3)))/12`

= `(-2+-sqrt76)/12`

i.e. either `costheta=(-2-8.7178)/12=-0.89315`

and `theta=153.27^@`

or `costheta=(-2+8.7178)/12=0.55982`

and `theta=55.96^@`