Question

Giải các PT sau:

a. sin x = sin \(\frac{\pi}{4}\)

b. sin x = \(\frac{1}{2}\)

c. cos x = \(\frac{\sqrt{2}}{2}\)

d. cos x = \(\frac{-\sqrt{2}}{2}\)

e. sin x = \(\frac{-1}{2}\)

Answer 1

a.

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+k2\pi\\x=\frac{3\pi}{4}+k2\pi\end{matrix}\right.\)

b.

\(\Leftrightarrow sinx=sin\left(\frac{\pi}{6}\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}+k2\pi\\x=\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)

c.

\(\Leftrightarrow cosx=cos\left(\frac{\pi}{4}\right)\)

\(\Leftrightarrow x=\pm\frac{\pi}{4}+k2\pi\)

d.

\(\Leftrightarrow cosx=cos\left(\frac{3\pi}{4}\right)\)

\(\Leftrightarrow x=\pm\frac{3\pi}{4}+k2\pi\)

e.

\(\Leftrightarrow sinx=sin\left(-\frac{\pi}{6}\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{6}+k2\pi\\x=\frac{7\pi}{6}+k2\pi\end{matrix}\right.\)