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Решение тригонометрических уравнений

Total questions: 12

Worksheet time: 43mins

Name
Class
Date
1.
a)

х=π5+2πn5, nϵZх=\frac{\pi}{5}+\frac{2\pi n}{5},\ n\epsilon Z

b)

х=π5+πn5, nϵZх=\frac{\pi}{5}+\frac{\pi n}{5},\ n\epsilon Z

c)

х=π5+2πn5, nϵZх=-\frac{\pi}{5}+\frac{2\pi n}{5},\ n\epsilon Z

2.
a)

х=π4+2πn, nϵZх=\frac{\pi}{4}+2\pi n,\ n\epsilon Z

b)

х=π4+πn2, nϵZх=\frac{\pi}{4}+\frac{\pi n}{2},\ n\epsilon Z

c)

х=π4+πn2, nϵZх=-\frac{\pi}{4}+\frac{\pi n}{2},\ n\epsilon Z

3.
a)

х=2π3+2πn, nϵZх=\frac{2\pi}{3}+2\pi n,\ n\epsilon Z

b)

х=2π3+2πn, nϵZх=-\frac{2\pi}{3}+2\pi n,\ n\epsilon Z

c)

х=±2π3+2πn, nϵZх=\pm\frac{2\pi}{3}+2\pi n,\ n\epsilon Z

d)

х=±2π3+πn, nϵZх=\pm\frac{2\pi}{3}+\pi n,\ n\epsilon Z

4.
a)

х=±π6+2πn, nϵZх=\pm\frac{\pi}{6}+2\pi n,\ n\epsilon Z

b)

х=π6+2πn, nϵZх=\frac{\pi}{6}+2\pi n,\ n\epsilon Z

c)

х=πn6, nϵZх=\frac{\pi n}{6},\ n\epsilon Z

5.
a)

х=±π3+2πn, nϵZх=\pm\frac{\pi}{3}+2\pi n,\ n\epsilon Z

b)

х=π3+πn, nϵZх=\frac{\pi}{3}+\pi n,\ n\epsilon Z

c)

х=±π3+πn, nϵZх=\pm\frac{\pi}{3}+\pi n,\ n\epsilon Z

6.
a)

х=πn, nϵZх=\pi n,\ n\epsilon Z

b)

х=π6+πn, nϵZх=\frac{\pi}{6}+\pi n,\ n\epsilon Z

c)

х=2π+πn, nϵZх=2\pi+\pi n,\ n\epsilon Z

7.
a)

х=π4+2πn, х=arctg2+πk, k,nϵZх=\frac{\pi}{4}+2\pi n,\ х=ar\operatorname{ctg}2+\pi k,\ k,n\epsilon Z

b)

х=π4+πn, х=arctg2+πk, n,kϵZх=\frac{\pi}{4}+\pi n,\ х=-ar\operatorname{ctg}2+\pi k,\ \ n,k\epsilon Z

c)

х=π4+2πk, х=arctg2+πk, kϵZх=\frac{\pi}{4}+2\pi k,\ х=-ar\operatorname{ctg}2+\pi k,\ k\epsilon Z

8.
a)

х=arctg2+πk, kϵZх=ar\operatorname{ctg}2+\pi k,\ k\epsilon Z

b)

х=arctg 23+πk, kϵZх=-ar\operatorname{ctg}\ \frac{2}{3}+\pi k,\ k\epsilon Z

c)

х=arctg 23+πk, kϵZх=ar\operatorname{ctg}\ \frac{2}{3}+\pi k,\ k\epsilon Z

9.
a)

х=arctg3+πn, х=arctg2+πk, k,nϵZх=ar\operatorname{ctg}3+\pi n,\ х=ar\operatorname{ctg}2+\pi k,\ k,n\epsilon Z

b)

х=arctg3+πn, х=arctg2+πk, k,nϵZх=-ar\operatorname{ctg}3+\pi n,\ х=-ar\operatorname{ctg}2+\pi k,\ k,n\epsilon Z

10.
a)

х=arctg3+πn, х=arctg2+πk, k,nϵZх=-ar\operatorname{ctg}3+\pi n,\ х=ar\operatorname{ctg}2+\pi k,\ k,n\epsilon Z

b)

х=arctg3+πn, х=arctg 12+2πn, nϵZх=-ar\operatorname{ctg}3+\pi n,\ х=ar\operatorname{ctg}\ \frac{1}{2}+2\pi n,\ n\epsilon Z

c)

х=arctg3+πn, х=arctg12+πn, nϵZх=-ar\operatorname{ctg}3+\pi n,\ х=ar\operatorname{ctg}\frac{1}{2}+\pi n,\ n\epsilon Z

11.
a)

нет корней

b)

х=π16+πn4, х=π4+πn, nZх=\frac{\pi}{16}+\frac{\pi n}{4},\ х=\frac{\pi}{4}+\pi n,\ n\in Z

c)

х=π4+πn4, х=π4+πn, nZх=\frac{\pi}{4}+\frac{\pi n}{4},\ х=\frac{\pi}{4}+\pi n,\ n\in Z

12.
a)

нет корней

b)

х=πn, nZх=\pi n,\ n\in Z

c)

х=πn2, nZх=\frac{\pi n}{2},\ n\in Z