Question

Giúp mình với

Answer 1

1.

Phương trình \(sinx=4\) vô nghiệm.

Answer 2

2.

\(sin\left(2x-\dfrac{\pi}{5}\right)=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\pi}{5}=\dfrac{\pi}{4}+k2\pi\\2x-\dfrac{\pi}{5}=\dfrac{3\pi}{4}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9\pi}{40}+k\pi\\x=\dfrac{19\pi}{40}+k\pi\end{matrix}\right.\)

Answer 3

3.

\(sin\left(\dfrac{\pi}{3}+x\right)=0\)

\(\Leftrightarrow\dfrac{\pi}{3}+x=k\pi\)

\(\Leftrightarrow x=-\dfrac{\pi}{3}+k\pi\)

Answer 4

4.

\(cos3x=-\dfrac{2}{3}\)

\(\Leftrightarrow3x=\pm arccos\left(-\dfrac{2}{3}\right)+k2\pi\)

\(\Leftrightarrow x=\pm\dfrac{1}{3}arccos\left(-\dfrac{2}{3}\right)+k2\pi\)

Answer 5

6.

\(cos\left(\dfrac{2\pi}{5}-\dfrac{x}{3}\right)=-1\)

\(\Leftrightarrow\dfrac{2\pi}{5}-\dfrac{x}{3}=\pi+k2\pi\)

\(\Leftrightarrow x=-\dfrac{9\pi}{5}+k2\pi\)

Answer 6

7.

ĐK: \(x\ne\dfrac{\pi}{2}+k\pi\)

\(tanx=tan\dfrac{4\pi}{5}\)

\(\Leftrightarrow x=\dfrac{4\pi}{5}+k\pi\)

Answer 7

8.

ĐK: \(x\ne\dfrac{\pi}{10}+\dfrac{k\pi}{5}\)

\(tan5x=2\Leftrightarrow5x=arctan2+k\pi\Leftrightarrow x=\dfrac{1}{5}arctan2+\dfrac{k\pi}{5}\)

Answer 8

9.

\(tan\left(2x-1\right)=\sqrt{3}\)

\(\Leftrightarrow2x-1=\dfrac{\pi}{3}+k\pi\)

\(\Leftrightarrow2x=\dfrac{\pi}{6}+\dfrac{1}{2}+\dfrac{k\pi}{2}\)