Do I use a double angle Identity?????

[missaurora1986]

Ok so I used the law of cosine to get to this answere cos 2(angle)=11/16. Now I need to find the angle. How do I do that?

 

[soroban]

Hello, missaurora1986!

\(\displaystyle \text{I used the law of cosine to get to this answer: }\:\cos 2\theta\:=\:\frac{11}{16}\)
\(\displaystyle \text{Now I need to find }\theta. \;\;\text{How do I do that?}\)

\(\displaystyle \text{You're right . . . use: }\;\cos2\theta \:=\:2\cos^2\!\theta - 1\)

\(\displaystyle \text{We have: }\;2\cos^2\!\theta - 1 \:=\:\frac{11}{16}\quad\Rightarrow\quad\cos^2\!\theta \:=\:\frac{27}{32}\quad\Rightarrow\quad\cos\theta \:=\:\pm\sqrt{\frac{27}{32}}\)

\(\displaystyle \text{Therefore: }\;\theta \;=\;\cos^{-1}\left(\frac{3\sqrt{6}}{8}\right)\)

 

[missaurora1986]

Thank you sooooooo much. That really helped