Question

use trigonometric identities to solve the following equation for 0 11 years ago

Answer 1

\(\normalsize\color{blue}{ 2(\sin θ)^2+\cos θ-1=0}\)
\(\normalsize\color{blue}{ 2(\sin^2θ)+\cos θ-1=0}\)
\(\normalsize\color{blue}{ 2(1-\cos^2θ)+\cos θ-1=0}\)
\(\normalsize\color{blue}{ 2-2\cos^2θ+\cos θ-1=0}\)
\(\normalsize\color{blue}{ -2\cos^2θ+\cos θ+1=0}\)

Answer 2

Let cos(theta) = a, and solve

Answer 3

\(\normalsize\color{blue}{ -2a^2+a+1=0}\)
\(\normalsize\color{blue}{ 2a^2-a-1=0}\)
\(\normalsize\color{blue}{ (2a+1)(a-1)=0}\)
\(\normalsize\color{blue}{a=~-½ ,~~~~1}\)

Answer 4

So, \(\normalsize\color{blue}{\cosθ=-1/2}\) or \(\normalsize\color{blue}{\cosθ=1}\)

Answer 5

Let me know if you need more help.

Answer 6

That's great. Thanks! I just needed the first one or two steps, but now I can compare and make sure I'm doing the rest of it correct. Thanks again.

Answer 7

Anytime, for the first step, just in case....
\(\normalsize\color{black}{\sin^2θ+\cos^2θ=1~~~~~~~~\rm identity}\)
and then you subtract cos²θ from both sides, to get that
\(\normalsize\color{black}{\sin^2θ=1-\cos^2θ}\) and then I substituted for sin²θ
to put everything in terms of cosines.

Answer 8

have fun :)