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16-апталық бақылау

Total questions: 15

Worksheet time: 28mins

Name
Class
Date
1.

cos(x2)<32\cos\left(\frac{x}{2}\right)<\frac{\sqrt[]{3}}{2}

a)

(π+5πk; 11π+5πk)\left(\pi+5\pi k;\ 11\pi+5\pi k\right)

b)

(π2+6πk; 11π6+6πk)\left(\frac{\pi}{2}+6\pi k;\ \frac{11\pi}{6}+6\pi k\right)

c)

(π3+7πk; 11π5+7πk)\left(\frac{\pi}{3}+7\pi k;\ \frac{11\pi}{5}+7\pi k\right)

d)

(π3+4πk; 12π7+4πk)\left(\frac{\pi}{3}+4\pi k;\ \frac{12\pi}{7}+4\pi k\right)

2.

3tg(x3+π6)10\sqrt[]{3}tg\left(\frac{x}{3}+\frac{\pi}{6}\right)-1\ge0

a)

[3πk; π+πk]\left[3\pi k;\ \pi+\pi k\right]

b)

(2πk; π+2πk)\left(2\pi k;\ \pi+2\pi k\right)

c)

[3πk; π+3πk)\left[3\pi k;\ \pi+3\pi k\right)

d)

(4πk; π+3πk)\left(4\pi k;\ \pi+3\pi k\right)

3.

tgx13tgx\ge\frac{1}{\sqrt[]{3}}

a)

(π4+2πk; π2+2πk)\left(\frac{\pi}{4}+2\pi k;\ \frac{\pi}{2}+2\pi k\right)

b)

(π6+πk; π2+πk]\left(\frac{\pi}{6}+\pi k;\ \frac{\pi}{2}+\pi k\right]

c)

[π6+πk; π2+πk)\left[\frac{\pi}{6}+\pi k;\ \frac{\pi}{2}+\pi k\right)

d)

[π3+πk; 3π2+πk)\left[\frac{\pi}{3}+\pi k;\ \frac{3\pi}{2}+\pi k\right)

4.

cosx12\cos x\le\frac{1}{2}

a)

[π3+2πn; 5π3+2πn]\left[\frac{\pi}{3}+2\pi n;\ \frac{5\pi}{3}+2\pi n\right]

b)

(π2+πn; 5π2+πn]\left(\frac{\pi}{2}+\pi n;\ \frac{5\pi}{2}+\pi n\right]

c)

[π3+2πn; 5π3+2πn]\left[\frac{\pi}{3}+2\pi n;\ \frac{5\pi}{3}+2\pi n\right]

d)

[π3+2πn; π2+2πn)\left[\frac{\pi}{3}+2\pi n;\ \frac{\pi}{2}+2\pi n\right)

5.

sinx>12\sin x>\frac{1}{\sqrt[]{2}}

a)

(π3+2πn; π+2πn)\left(\frac{\pi}{3}+2\pi n;\ \pi+2\pi n\right)

b)

(π4+πn; 3π4+πn)\left(\frac{\pi}{4}+\pi n;\ \frac{3\pi}{4}+\pi n\right)

c)


(π4+2πn; 3π4+2πn)\left(\frac{\pi}{4}+2\pi n;\ \frac{3\pi}{4}+2\pi n\right)

d)

(π2+2πn; 3π2+2πn)\left(\frac{\pi}{2}+2\pi n;\ \frac{3\pi}{2}+2\pi n\right)

6.

sinx22\sin x\le\frac{\sqrt[]{2}}{2}

a)

[5π4+2πk; π4+2πk]\left[-\frac{5\pi}{4}+2\pi k;\ \frac{\pi}{4}+2\pi k\right]

b)

[5π4+πk; π4+πk)\left[-\frac{5\pi}{4}+\pi k;\ -\frac{\pi}{4}+\pi k\right)

c)

(3π4+2πk; π4+2πk]\left(-\frac{3\pi}{4}+2\pi k;\ \frac{\pi}{4}+2\pi k\right]

d)

(3π4+πk; π4+πk)\left(-\frac{3\pi}{4}+\pi k;\ \frac{\pi}{4}+\pi k\right)

7.

2sin3x<12\sin3x<1

a)

(7π18+πk3;π18+πk3)\left(\frac{7\pi}{18}+\frac{\pi k}{3};-\frac{\pi}{18}+\frac{\pi k}{3}\right)

b)

(7π18+2πk3;π18+2πk3)\left(-\frac{7\pi}{18}+\frac{2\pi k}{3};\frac{\pi}{18}+\frac{2\pi k}{3}\right)

c)

(5π18+πk3;π18+πk3)\left(-\frac{5\pi}{18}+\frac{\pi k}{3};\frac{\pi}{18}+\frac{\pi k}{3}\right)

d)

(3π17+2πk3;π17+2πk3)\left(-\frac{3\pi}{17}+\frac{2\pi k}{3};\frac{\pi}{17}+\frac{2\pi k}{3}\right)

8.

sin(2x3)>12\sin\left(2x-3\right)>-\frac{1}{2}

a)

5π1232+2πn-\frac{5\pi}{12}-\frac{3}{2}+2\pi n

7π13+52+2πn\frac{7\pi}{13}+\frac{5}{2}+2\pi n

b)

π12+32+πn-\frac{\pi}{12}+\frac{3}{2}+\pi n

7π12+32+πn\frac{7\pi}{12}+\frac{3}{2}+\pi n

c)

5π12+52+πn\frac{5\pi}{12}+\frac{5}{2}+\pi n

5π12+72+2πn-\frac{5\pi}{12}+\frac{7}{2}+2\pi n

9.

sin(x+π4)>22\sin\left(x+\frac{\pi}{4}\right)>\frac{\sqrt[]{2}}{2}

a)

(πn; π6+πn)\left(\pi n;\ \frac{\pi}{6}+\pi n\right)

b)

(2πn; π2+2πn)\left(2\pi n;\ \frac{\pi}{2}+2\pi n\right)

c)

(πn; π3+πn)\left(\pi n;\ \frac{\pi}{3}+\pi n\right)

d)

(πn; π4+2πn)\left(\pi n;\ \frac{\pi}{4}+2\pi n\right)

10.

I және II ширектерде таңбасы оң болатын функцияны көрсет

a)

sina

b)

cosa

c)

tga

d)

ctga

11.

Жұп функцияны көрсет:

a)

sin(-a)

b)

cos(-a)

c)

tg(-a)

d)

ctg(-a)

12.

3tg(4xπ3)3<03tg\left(-4x-\frac{\pi}{3}\right)-3<0  

a)

[7π48+πk4;π24+πk4]\left[\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{\pi}{24}+\frac{\pi k}{4}\right]  

b)

(7π48+πk4;5π24+πk4)\left(\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{5\pi}{24}+\frac{\pi k}{4}\right)  

c)

(7π48+πk4;π24+πk4)\left(\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{\pi}{24}+\frac{\pi k}{4}\right)  

d)

(7π48+πk4;π24+πk4]\left(\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{\pi}{24}+\frac{\pi k}{4}\right]  

13.

cos2x>32\cos2x>-\frac{\sqrt{3}}{2}  

a)

(5π12+2πn2;5π4+2πn2;)\left(-\frac{5\pi}{12}+\frac{2\pi n}{2};\frac{5\pi}{4}+\frac{2\pi n}{2};\right)  

b)

(5π12+2πn2;5π12+2πn2;)\left(-\frac{5\pi}{12}+\frac{2\pi n}{2};\frac{5\pi}{12}+\frac{2\pi n}{2};\right)  

c)

(π12+2πn;π4+2πn;)\left(-\frac{\pi}{12}+2\pi n;\frac{\pi}{4}+2\pi n;\right)  

d)

(2π3+2πn2;2π3+2πn2;)\left(-\frac{2\pi}{3}+\frac{2\pi n}{2};\frac{2\pi}{3}+\frac{2\pi n}{2};\right)  

14.

5π6\frac{5\pi}{6}  радианды градусқа айналдыр

a)

150

b)

300

c)

120

d)

180

15.

Негізгі тригонометриялық тепе - теңдікті көрсетіңдер:

a)

sinx+cosx=1\sin x+\cos x=1

b)

sin2x+cos2x=1\sin^2x+\cos^2x=1

c)

sin2x+cos2y=1\sin^2x+\cos^2y=1

d)

sin2xcos2x=1\sin^2x-\cos^2x=1