Free Printable Тригонометрия

1.

4 cos 45 ctg 60 tg30-3sin 45

a)

$\frac{3}{5}$

b)

$\frac{\sqrt[]{5}}{6}$

c)

$-\frac{5\sqrt[]{2}}{6}$

d)

$\frac{5}{6}$

2.

$tg\left(-\frac{\pi}{4}\right)\ \sin\left(-\frac{\pi}{3}\right)\ \operatorname{ctg}\left(-\frac{\pi}{6}\right)$

a)

1,5

b)

-1,5

c)

-1

d)

1

3.

-cos²a+1-sin²a

a)

-1

b)

1

c)

2

d)

0

4.

(cos a-1)(cos a+1)

a)

sin a

b)

-sin² a

c)

cos a

d)

cos² a

5.

1-cos a sin a ctg a

a)

sin² a

b)

cos² a

c)

sin a

d)

cos a

6.

$\frac{1-\cos^{2\ ^{ }}\beta}{1-\sin^2\beta}$

a)

sin b

b)

cos b

c)

ctg b

d)

tg² $\beta$

7.

$\cos\ a-\frac{1-\sin^2a}{\cos\ a\ }$

a)

cos a

b)

-1

c)

0

d)

1

8.

$\frac{\cos^{3\ }a-\sin^{3\ }a}{1+\cos a\ \cdot\sin\ a}$

a)

cos a

b)

cos a-sin a

c)

sin a

d)

cos a+sin a

9.

sin⁴ a (1+tg² a) +sin²a

a)

sin a

b)

cos a

c)

ctg² a

d)

tg² a

10.

cos a=-0,6 және 180<a<270 болса, 2sin²a -3tg a мәнін табыңыз.

a)

2

b)

-2 $\frac{18}{25}$

c)

18/25

d)

-2

11.

$\frac{сos135\cdot\sin\ 240\cdot\operatorname{ctg}\ 210}{\operatorname{ctg}\ 405\cdot tg330\cdot\sin450}$

a)

1/3

b)

$\frac{-3\sqrt[]{6}}{4}$

c)

3/4

d)

$\sqrt[]{6}$

12.

$\frac{\sin\left(a-\frac{\pi}{2}\right)\cos\left(-a-\pi\right)tg\left(\frac{3\pi}{2}-a\right)}{\cos\left(a-2\pi\right)\operatorname{ctg}\left(a-\pi\right)}$

a)

sin a

b)

-cos a

c)

cos a

d)

-tg a

13.

Қосу формуласын пайдаланып есептеңіз: sin 105

a)

$\frac{\sqrt[]{2}}{4}$

b)

$\frac{\sqrt[]{6}+\sqrt[]{2}}{4}$

c)

$\frac{\sqrt[]{3}}{2}$

d)

$\frac{\sqrt[]{6}}{4}$

14.

cos 109 sin19-cos19 sin 109

a)

1

b)

-2

c)

0

d)

-1

15.

$\frac{\cos\left(x+15\right)-\cos x\cdot\cos15}{\sin x\cdot\cos15}$

a)

-2

b)

2

c)

$\sqrt[]{3}-2$

d)

$\sqrt[]{3}$

16.

Қос бұрыштың формулаларын қолданып ықшамдаңыз: 2sin105cos105

a)

-1

b)

-2

c)

$\frac{1}{2}$

d)

- $\frac{1}{2}$

17.

cos⁴ x-sin⁴ x

a)

1

b)

cos2x

c)

-1

d)

sin 2x

18.

$\frac{\sin130+\sin110}{\cos130+\cos110}$

a)

-3

b)

3

c)

- $\sqrt[]{3}$

d)

$\sqrt[]{3}$

19.

Тригонометриялық теңдеулерді шешіңіз: 2sin² x-3sin x-2=0

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{3}+2\pi n$

c)

(-1)ⁿ⁺¹ $\frac{\pi}{6}+\pi n$

d)

$\frac{\pi}{6}+\pi n\$

20.

sin² x-4sinxcosx+3cos² x=0

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{4}+\pi n;ar\operatorname{ctg}3+\pi n$

c)

$\frac{\pi}{3}+\pi n$

d)

$ar\operatorname{ctg}2+\pi n$

21.

cosx-cos5x=2sin3x

a)

$\pi n$

b)

$\frac{\pi n}{3};\frac{\pi}{4}\left(4k+1\right)$

c)

$\frac{\pi}{3}+\pi n$

d)

$\frac{\pi}{4}$

22.

$\sqrt[]{3}-2\cos x\ge0$

a)

$\left[-\frac{\pi}{6};\frac{\pi}{6}\right]$

b)

$\left[0;\frac{\pi}{6}\right]$

c)

$\left[\frac{\pi}{6}+2\pi n;\frac{11\pi}{6}+2\pi n\right]$

d)

$\left[\frac{\pi}{3};\frac{\pi}{2}\right]$

23.

$2\sin\left(x-\frac{\pi}{3}\right)\le\sqrt[]{3}$

a)

$\left(0;\pi\right)$

b)

$\left(\pi;\frac{\pi}{3}\right)$

c)

$\left[-\pi;\frac{2\pi}{3}\right]$

d)

$\left[-\pi+2\pi n;\frac{2\pi}{3}+2\pi n\right]$

24.

$tg\left(x+\frac{\pi}{4}\right)\ge1$

a)

(-1;0)

b)

(0;1)

c)

$\left(\frac{\pi}{4};\pi n\right)$

d)

$\left[\pi n;\frac{\pi}{4}+\pi n\right)$

25.

$3\operatorname{ctg}\left(\frac{\pi}{6}+\frac{x}{2}\right)>-\sqrt[]{3}$

a)

$\left(-\pi:0\right)$

b)

$-\frac{\pi}{3}+2\pi n<x<\pi+2\pi n$

c)

$\left(\frac{\pi}{3};\pi\right)$

d)

$\left(0;\pi\right)$

Тригонометрия

Total questions: 25

Worksheet time: 13mins

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