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Тригонометриялық теңдеулер

Authored by Мухамбет Забыханов

Mathematics

10th Grade

Used 169+ times

Тригонометриялық теңдеулер
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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 sin⁡x=a\sin x=a  тригонометриялық теңдеуінің шешімінің жалпы түрі

 x=(−1)narcsin⁡a+πn, n∈Zx=\left(-1\right)^n\arcsin a+\pi n,\ n\in Z  

 x=±arccos⁡a+2πn, n∈Zx=\pm\arccos a+2\pi n,\ n\in Z  

 x=π2+2πn, n∈Zx=\frac{\pi}{2}+2\pi n,\ n\in Z  

 x=−π4+πn, n∈Zx=-\frac{\pi}{4}+\pi n,\ n\in Z  

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 cos⁡x=a \cos x=a\   тригонометриялық теңдеуінің шешімінің жалпы түрі

 x=arccos⁡a+πn, n∈Zx=\arccos a+\pi n,\ n\in Z  

 x=±arccos⁡a+2πn, n∈Zx=\pm\arccos a+2\pi n,\ n\in Z  

 x=arccos⁡a+2πn, n∈Zx=\arccos a+2\pi n,\ n\in Z  

 x=π2+2πn, n∈Zx=\frac{\pi}{2}+2\pi n,\ n\in Z  

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 tgx=a tgx=a\   теңдеуінің шешімі

 x=arctg⁡a+πn, n∈Zx=ar\operatorname{ctg}a+\pi n,\ n\in Z  

 x=arcctg⁡a +πn, n∈Zx=\operatorname{arcctg}a\ +\pi n,\ n\in Z  

 x=arctg⁡a+2πn, n∈Zx=ar\operatorname{ctg}a+2\pi n,\ n\in Z  

 x=arcctg⁡a +2πn, n∈Zx=\operatorname{arcctg}a\ +2\pi n,\ n\in Z  

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

 ctg⁡x=a\operatorname{ctg}x=a  теңдеуінің шешімі

 x=arctg⁡a+πn, n∈Zx=ar\operatorname{ctg}a+\pi n,\ n\in Z  

 x=arctg⁡a+2πn, n∈Zx=ar\operatorname{ctg}a+2\pi n,\ n\in Z  

 x=arcctg⁡a+πn, n∈Zx=\operatorname{arcctg}a+\pi n,\ n\in Z  

 x=arcctg⁡a+2πn, n∈Zx=\operatorname{arcctg}a+2\pi n,\ n\in Z  

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

 2sin⁡x=12\sin x=1  теңдеуінің шешімі

 x=(−1)n π6+πn, n∈Zx=\left(-1\right)^n\ \frac{\pi}{6}+\pi n,\ n\in Z  

 x=(−1)n π3+πn, n∈Zx=\left(-1\right)^n\ \frac{\pi}{3}+\pi n,\ n\in Z  

 x=(−1)n+1 π3+2πn, n∈Zx=\left(-1\right)^{n+1}\ \frac{\pi}{3}+2\pi n,\ n\in Z  

 x=(−1)n π6+2πn, n∈Zx=\left(-1\right)^n\ \frac{\pi}{6}+2\pi n,\ n\in Z  

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

 cos⁡x=32\cos x=\frac{\sqrt{3}}{2}  теңдеуінің шешімі

 x=±π6+2πk, k∈Zx=\pm\frac{\pi}{6}+2\pi k,\ k\in Z  

 x=±π6+πk, k∈Zx=\pm\frac{\pi}{6}+\pi k,\ k\in Z  

 x=±π3+2πk, k∈Zx=\pm\frac{\pi}{3}+2\pi k,\ k\in Z  

 x=±2π3+2πk, k∈Zx=\pm\frac{2\pi}{3}+2\pi k,\ k\in Z  

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

 tgx=34tgx=\frac{3}{4}  теңдеуінің шешімі

 x=arctg⁡ 43+πk, k∈Zx=ar\operatorname{ctg}\ \frac{4}{3}+\pi k,\ k\in Z  

 x=arcctg⁡ 34+πk, k∈Zx=\operatorname{arcctg}\ \frac{3}{4}+\pi k,\ k\in Z  

 x=arctg⁡ 34+πk, k∈Zx=ar\operatorname{ctg}\ \frac{3}{4}+\pi k,\ k\in Z  

 x=arctg⁡ 34+π2k, k∈Zx=ar\operatorname{ctg}\ \frac{3}{4}+\frac{\pi}{2}k,\ k\in Z  

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