Trigonometric equation: solving sin 2theta = cos 7pi/4

[Guest]

Has someone already solved this equation?

sin 2theta = cos 7pi/4?

 

[stapel]

Has someone already solved this equation?

Probably, but I doubt that this is a problem of significance, such that any records were kept. Why?

Eliz.

 

[soroban]

Hello, americo74!

Do you mean "at this site recently"?
I don't recall seeing it.

\(\displaystyle \L\sin 2\theta \:= \;\cos\frac{7\pi}{4}\)

We have: \(\displaystyle \L\:\sin2\theta \;=\;\frac{\sqrt{2}}{2}\)

Then: \(\displaystyle \L\:2\theta \;=\;\begin{Bmatrix}\frac{\pi}{4}\,+\,2k\pi \\ \frac{3\pi}{4}\,+\,2k\pi\end{Bmatrix}\)

Therefore: \(\displaystyle \L\:\theta \;=\;\begin{Bmatrix}\frac{\pi}{8}\,+\,k\pi \\ \frac{3\pi}{8}\,+\,k\pi\end{Bmatrix}\)

 

[Guest]

Thank you Soroban. One day I might be like you!