Can you show me how to solve this?

2 cos^2 (theta) - 3 cos (theta) +1 = 0

Question

Can you show me how to solve this?

2 cos^2 (theta) - 3 cos (theta) +1 = 0

anonymous · Answer

Quadratic in cos theta (let cos theta = x)

anonymous · Answer

still need help here?

anonymous · Answer

yes please, how do you combine the cos so you can solve?

anonymous · Answer

do what @estudier  said... this trigonometric equation is an equation in quadratic form... and you do know how to solve quadratic equations...

using his substitution of $\large x=cos\theta $,
$$\huge 2cos^2\theta-3cos\theta+1=0\rightarrow 2x^2-3x+1=0 $$
can you solve that equation in x?

anonymous · Answer

so just factor it out?

anonymous · Answer

yes... that's one way....:)

anonymous · Answer

hello?

anonymous · Answer

sorry, after i factor i don't see how i can relate it to the unit circle (my answer should be $$0\le \Theta \le2\pi$$

anonymous · Answer

@dpaInc showed you already how it's done correctly, nevertheless here are the final steps in case you still have trouble, you find solutions in terms of x, therefore you have to use Back-Substitution:

$$x_1=\cos \theta=1 \x_2=\cos\theta=\frac{1}{2}$$