ĐGTD ĐH Bách khoa - Tư duy Toán học - Phương trình lượng giác cơ bản

m = −3

m = −2

m = 0

m = 3

$[\begin{array}{c}x=\alpha +k\pi \\ x=\pi -\alpha +k\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\alpha +k2\pi \\ x=\pi -\alpha +k2\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\alpha +k2\pi \\ x=-\alpha +k2\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\alpha +k\pi \\ x=-\alpha +k\pi \end{array}\left(k\in Z\right)$

$x=-\frac{\pi }{2}+k\pi \left(k\in Z\right)$

$x=\frac{\pi }{2}+k\pi \left(k\in Z\right)$

$x=-\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$x=-\pi +k2\pi \left(k\in Z\right)$

$x=\frac{5\pi }{6}+k2\pi$

$x=\frac{\pi }{6}$

$x=\frac{5\pi }{6}$

$x=\frac{\pi }{3}$

1

0

3

2

$x=k\pi \left(k\in Z\right)$

$x=\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$x=k2\pi \left(k\in Z\right)$

$x=\frac{\pi }{2}+k\pi \left(k\in Z\right)$

$\sin x=-1\iff x=-\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$\sin x=0\iff x=k\pi \left(k\in Z\right)$

$\sin x=0\iff x=k2\pi \left(k\in Z\right)$

$\sin x=1\iff x=\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$x=\frac{\pi }{2}+k2\pi$

$x=\frac{k\pi }{2}$

$x=k2\pi$

$x=\frac{\pi }{6}+k2\pi$

$\cos x\ne 1\iff x\ne \frac{\pi }{2}+k\pi \left(k\in Z\right)$

$\cos x\ne 0\iff x\ne \frac{\pi }{2}+k\pi \left(k\in Z\right)$

$\cos x\ne -1\iff x\ne -\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$\cos x\ne 0\iff x\ne \frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{6}+k2\pi \\ x=\frac{5\pi }{6}+k2\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{6}+k2\pi \\ x=-\frac{\pi }{6}+k2\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{3}+k2\pi \\ x=\frac{2\pi }{3}+k2\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{3}+k2\pi \\ x=-\frac{\pi }{3}+k2\pi \end{array}\left(k\in Z\right)$

0

2

1

3

$k2\pi \left(k\in Z\right)$

$k2\pi ;\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$\frac{k\pi }{2}\left(k\in Z\right)$

$k\pi ;\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$x=\frac{\pi }{2}$

$x=\pi$

x = 0

$x=-\frac{\pi }{2}$

$x=\frac{\pi }{3}+k\pi \left(k\in Z\right)$

$x=-\frac{\pi }{3}+k2\pi \left(k\in Z\right)$

$x=\frac{\pi }{6}+k\pi \left(k\in Z\right)$

$x=-\frac{\pi }{3}+k\pi \left(k\in Z\right)$

k2π (k∈Z)

kπ (k∈Z)

π + k2π (k∈Z)

Cả 3 đáp án đúng

$x=\frac{\pi }{8}+k\pi \left(k\in Z\right)$

$x=\frac{\pi }{8}+\frac{k\pi }{5}\left(k\in Z\right)$

$x=\frac{\pi }{8}+\frac{k\pi }{4}\left(k\in Z\right)$

$x=\frac{\pi }{8}+\frac{k\pi }{2}\left(k\in Z\right)$

$x=-30°$

$x=-60°$

$x=30°$

$x=-60°,x=30°$

$x=\frac{k\pi }{2}\left(k\in Z\right)$

$x=k\pi \left(k\in Z\right)$

$x=k2\pi \left(k\in Z\right)$

Kết quả khác

D = R\ $\left\{\frac{\pi }{6}+k\frac{\pi }{2};\frac{\pi }{4}+k\frac{\pi }{2}|k\in Z\right\}$

D = R\ $\left\{-\frac{\pi }{3}+k\pi ;\frac{\pi }{2}+k\pi |k\in Z\right\}$

D = R\ $\left\{-\frac{\pi }{6}+k\frac{\pi }{2}|k\in Z\right\}$

D = R\ $\left\{-\frac{\pi }{6}+k\frac{\pi }{2};\frac{\pi }{4}+k\frac{\pi }{2}|k\in Z\right\}$

8

6

2

4

– 1 < m < 0

– 3 < m < - 1

$[\begin{array}{c}m<1\\ m>2\end{array}$

$[\begin{array}{c}m<-2\\ m>0\end{array}$

$[\begin{array}{c}x=\frac{\pi }{48}+\frac{k\pi }{2}\\ x=-\frac{5\pi }{24}+k\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{48}+k\pi \\ x=-\frac{5\pi }{12}+k2\pi \end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{24}+k\pi \\ x=-\frac{5\pi }{48}+\frac{k\pi }{2}\end{array}\left(k\in Z\right)$

$[\begin{array}{c}x=\frac{\pi }{24}+k2\pi \\ x=-\frac{5\pi }{48}+k\pi \end{array}\left(k\in Z\right)$

$x=\frac{\pi }{8}+\frac{k\pi }{2},x=\frac{\pi }{4}+k\pi \left(k\in Z\right)$

$x=k2\pi ,x=\frac{\pi }{2}+k2\pi \left(k\in Z\right)$

$x=k\pi ,x=\frac{\pi }{4}+k\pi \left(k\in Z\right)$

$x=\frac{\pi }{8}+\frac{k\pi }{2},x=-\frac{\pi }{4}+k\pi \left(k\in Z\right)$

R\$\left\{\frac{k\pi }{2},k\in Z\right\}$

R\$\left\{\frac{\pi }{2}+k\pi ,k\in Z\right\}$

R\$\left\{k\pi ,k\in Z\right\}$

R

$x=\frac{k\pi }{6},x=\frac{k\pi }{10}$

$x=\frac{k\pi }{6},x=\frac{k\pi }{20}$

$x=\frac{k\pi }{3},x=\frac{k\pi }{20}$

$x=\frac{k\pi }{3},x=\frac{k\pi }{10}$

980

51

981

1000

$[\begin{array}{c}m=1\\ m=\frac{1}{2}\end{array}$

$[\begin{array}{c}m=-\frac{3}{2}\\ m=0\end{array}$

$[\begin{array}{c}m=-\frac{1}{4}\\ m=\frac{2}{3}\end{array}$

$[\begin{array}{c}m=-\frac{1}{2}\\ m=\frac{1}{3}\end{array}$

$x=\frac{\pi }{6}+k2\pi$

Vô nghiệm

$x=-\frac{\pi }{6}+k2\pi$

$x=\pm \frac{\pi }{6}+k2\pi$

$k\pi ,k\in Z$

$\frac{\pi }{4}+\frac{k\pi }{2},k\in Z$

$\frac{k\pi }{2},k\in Z$

Vô nghiệm

$x=\frac{\pi }{4}+k2\pi \left(k\in Z\right)$

$x=\frac{\pi }{4}+k\pi \left(k\in Z\right)$

$x=\frac{\pi }{4}+\frac{k\pi }{2}\left(k\in Z\right)$

$x=-\frac{\pi }{4}+k\pi \left(k\in Z\right)$

$m\in \left(0;1\right]\cup \left[\frac{3}{2};+\infty \right)$

$m\in \left(-\infty ;1\right]\cup \left[\frac{3}{2};+\infty \right)$

$m\in \left(0;\frac{1}{2}\right]\cup \left[1;\frac{3}{2}\right)$

$m\in \left[0;1\right)\cup \left[\frac{3}{2};2\right)$