Phương trình lượng giác.:confused::confused:

L

lan_phuong_000

Đây là những dạng bài rất cơ bản nha bạn! :)
1. sin(π4+4)=sin(2x−π4)sin(\dfrac{\pi}{4} + 4)=sin(2x - \dfrac{\pi}{4})
\Leftrightarrow [π4+4=2x−π4+k2ππ4+4=π−2x+π4\left[\begin{matrix}\dfrac{\pi}{4} + 4=2x - \dfrac{\pi}{4} + k2\pi\\ \dfrac{\pi}{4} + 4= \pi - 2x + \dfrac{\pi}{4} \end{matrix}\right.

\Leftrightarrow [x=π2+k2πx=π3+k.2π3\left[\begin{matrix}x= \dfrac{\pi}{2} + k2\pi\\ x=\dfrac{\pi}{3} + k.\dfrac{2\pi}{3} \end{matrix}\right.

2. sinx.(sin2x−1)=0sinx.(sin2x -1)=0 (giải như giải pt tích)
\Leftrightarrow [sinx=0sin2x=1\left[\begin{matrix}sinx=0\\ sin2x =1 \end{matrix}\right.

\Leftrightarrow [x=kπ2x=π2+k2π\left[\begin{matrix}x= k\pi\\ 2x = \dfrac{\pi}{2} + k2\pi \end{matrix}\right.

\Leftrightarrow [x=kπx=π4+kπ\left[\begin{matrix}x= k\pi\\ x = \dfrac{\pi}{4} + k\pi \end{matrix}\right.

3. sin(x−120)−cos2x=0sin(x - 120) - cos2x = 0 (sd ct cosx=sin(90−x)cosx=sin(90 - x))
\Leftrightarrow $sin(x - 120) = sin(90 - 2x}$

\Leftrightarrow [x−120=90−2x+k.360x−120=180−90+2x+k.360\left[\begin{matrix}x - 120 = 90 - 2x + k.360 \\ x - 120 = 180 - 90 + 2x + k.360 \end{matrix}\right.

\Leftrightarrow [x=70+k.120x=−210−k.360\left[\begin{matrix}x = 70 + k.120\\ x = -210 - k.360\end{matrix}\right.

4. sin(x+2π3)=cos3xsin(x + \dfrac{2\pi}{3}) = cos3x (tương tự bài 3)
\Leftrightarrow sin(x+2π3)=sin(π2−3x)sin(x + \dfrac{2\pi}{3}) = sin(\dfrac{\pi}{2} - 3x)

\Leftrightarrow [x+2π3=π2−3x+k2πx+2π3=π−π2+3x+k2π\left[\begin{matrix} x + \dfrac{2\pi}{3} = \dfrac{\pi}{2} - 3x + k2\pi \\ x + \dfrac{2\pi}{3}= \pi - \dfrac{\pi}{2} + 3x + k2\pi \end{matrix}\right.

\Leftrightarrow [x=−π24+k.π2x=π12−k.π2\left[\begin{matrix}x= \dfrac{-\pi}{24} + k.\dfrac{\pi}{2}\\ x= \dfrac{\pi}{12} - k.\dfrac{\pi}{2} \end{matrix}\right.



 
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