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Жаңа тригонометрия Балмира

Authored by Darhan Tynyshtyk

Mathematics

11th Grade

Used 17K+ times

Жаңа тригонометрия Балмира
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23 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 4sin⁡33x−sin⁡3x=2+sin⁡3x4\sin^33x-\sin3x=2+\sin^3x  

 x=π3+2π x=\frac{\pi}{3}+2\pi\   

 x=π6+2πn3; x=(−1)k+1 13arcsin⁡ 23+πn3x=\frac{\pi}{6}+\frac{2\pi n}{3};\ x=\left(-1\right)^{k+1}\ \frac{1}{3}\arcsin\ \frac{2}{3}+\frac{\pi n}{3}  

 x=π6+π3 x= arcsin⁡ 13+2πx=\frac{\pi}{6}+\frac{\pi}{3}\ x=\ \arcsin\ \frac{1}{3}+2\pi  

 x=π6+2π3n ; x=23arcsin⁡13+πn3x=\frac{\pi}{6}+\frac{2\pi}{3}n\ ;\ x=\frac{2}{3}\arcsin\frac{1}{3}+\frac{\pi n}{3}  

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 2cos⁡2x−5cos⁡x=−32\cos^2x-5\cos x=-3  

 2πn2\pi n  

 4πn4\pi n  

 πn\pi n  

 π2\frac{\pi}{2}  

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 cos⁡23x=12\cos^23x=\frac{1}{2}  

 π6+πk6\frac{\pi}{6}+\frac{\pi k}{6}  

 π12+πk6\frac{\pi}{12}+\frac{\pi k}{6}  

 π4+πn6\frac{\pi}{4}+\frac{\pi n}{6}  

 π8+πn8\frac{\pi}{8}+\frac{\pi n}{8}  

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 2cos⁡2x+3=02\cos2x+\sqrt{3}=0  

 x=±5π12+πkx=\pm\frac{5\pi}{12}+\pi k  

 x=5π12x=\frac{5\pi}{12}  

 x=±π12+πkx=\pm\frac{\pi}{12}+\pi k  

 x=±5π12+2πkx=\pm\frac{5\pi}{12}+2\pi k  

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 6sin⁡2x−cos⁡x−5=06\sin^2x-\cos x-5=0  

 x= arccos⁡ 13+πkx=\ \arccos\ \frac{1}{3}+\pi k  

 x=±4π3+2πkx=\pm\frac{4\pi}{3}+2\pi k  

 x=±2π3+2πn ; x=arccos⁡ 13+2πkx=\pm\frac{2\pi}{3}+2\pi n\ ;\ x=\arccos\ \frac{1}{3}+2\pi k  

 x=±π3+πk; x=arccos⁡ 13+2πkx=\pm\frac{\pi}{3}+\pi k;\ x=\arccos\ \frac{1}{3}+2\pi k  

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 6cos⁡2x+sin⁡x−5=06\cos^2x+\sin x-5=0  

 x=2π3+πkx=\frac{2\pi}{3}+\pi k  

 x=(−1)k  π6+2πk;  arcsin⁡ 13+2ππkx=\left(-1\right)^{k\ }\ \frac{\pi}{6}+2\pi k;\ \ \arcsin\ \frac{1}{3}+2\pi\pi k  

 x=π6+πk; 2π3+πnx=\frac{\pi}{6}+\pi k;\ \frac{2\pi}{3}+\pi n  

 x=(−1)k π6+πn ;(−1)k+1 arcsin⁡ 13+πnx=\left(-1\right)^k\ \frac{\pi}{6}+\pi n\ ;\left(-1\right)^{k+1\ }\arcsin\ \frac{1}{3}+\pi n  

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 (2sin⁡ x2−2 cos⁡ x2)2=5+sin⁡ (x4−x2)\left(\sqrt{2}\sin\ \frac{x}{2}-\sqrt{2\ }\cos\ \frac{x}{2}\right)^2=5+\sin\ \left(\frac{x}{4}-\frac{x}{2}\right)  

 π2+πk\frac{\pi}{2}+\pi k  

 3π2+4πk\frac{3\pi}{2}+4\pi k  

 5π6+4πk\frac{5\pi}{6}+4\pi k  

 π6+πk\frac{\pi}{6}+\pi k  

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