Free Printable МАТЕМАТИКА 3-АЙ 3-АПТА

1.

Теңдеуді шешеіңіз: sinx=0

a)

x = π/2 + 2πk

b)

x = π + 2πk

c)

x = 2πk

d)

x = πk

2.

Қай теңдеудің шешімі жоқ?

a)

cos x = 0,5

b)

tg x =1

c)

sin x = π

d)

cos x = -2

3.

Шешімі х = ±arcsin a + пn, n ϵ Z болатын теңдеуді көрсетіңіз:

a)

cos x = a

b)

sin x = a

c)

ctg x = a

d)

tg x = a

4.

cos2x – 3sinx + 1 = 0

a)

$\frac{\pi}{6}+2\pi\kappa$

b)

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

c)

$\frac{\pi}{4}+2\pi\kappa$

d)

$\frac{\pi}{2}+2\pi\kappa$

5.

Тригонометриялық теңдеу болатын теңдеуді көрсетіңіз:

a)

sin ⁡x = 0

b)

3x - 8 = 12

c)

ху+ 5х = 0

d)

ху+ 10= 0

6.

cos⁡ x = a және sin ⁡х = a теңдеулерінің шешімі бар, егер a … болса:

a)

-1 ≤ а ≤ 1

b)

а >1

c)

а ≤ 1

7.

𝑠𝑖𝑛𝑥 = −1

a)

$\frac{\pi}{4}+2\pi n,\ n\in Z$

b)

$-\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

8.

𝑡g𝑥 = −1

a)

$-\frac{\pi}{4}+\pi n,\ n\in Z$

b)

$-\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

9.

𝑐𝑡g𝑥 = −1

a)

$-\frac{\pi}{4}+\pi n,\ n\in Z$

b)

$\frac{3\pi}{4}+\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

10.

𝑐𝑜𝑠𝑥 = 1

a)

$2\pi n,\ n\in Z$

b)

$-\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

11.

𝑠𝑖𝑛𝑥 = 1

a)

$\frac{\pi}{4}+2\pi n,\ n\in Z$

b)

$\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

12.

𝑐𝑜𝑠𝑥 = −1

a)

$\pi+2\pi n,\ n\in Z$

b)

$\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

13.

𝑡g𝑥 = 0

a)

$\pi+2\pi n,\ n\in Z$

b)

$\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

14.

c𝑡g𝑥 = 0

a)

$\pi+2\pi n,\ n\in Z$

b)

$\frac{\pi}{2}+2\pi n,\ n\in Z$

c)

𝑥 = 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = 2𝜋𝑛, 𝑛 ∈ Z

15.

𝑐𝑜𝑠𝑥 = 𝑎 − 1 ≤ 𝑎 ≤ 1

a)

$𝑥=(−1)^n\arcsin a+\pi n$

b)

$𝑥=(−1)^{1+n}\arcsin a+\pi n$

c)

𝑥 = ±𝑎𝑟𝑐𝑐𝑜𝑠𝑎 + 2𝜋n

d)

𝑥 = ±(𝜋 − 𝑎𝑟𝑐𝑠𝑖𝑛𝑎) + 2𝜋n

16.

𝑠𝑖𝑛𝑥 = −a − 1 ≤ 𝑎 ≤ 1

a)

$𝑥=(−1)^n\arcsin a+\pi n$

b)

$𝑥=(−1)^{1+n}\arcsin a+\pi n$

c)

𝑥 = ±𝑎𝑟𝑐𝑐𝑜𝑠𝑎 + 2𝜋n

d)

𝑥 = ±(𝜋 − 𝑎𝑟𝑐𝑠𝑖𝑛𝑎) + 2𝜋n

17.

𝑐𝑜𝑠𝑥 = −a , − 1 ≤ 𝑎 ≤ 1

a)

$𝑥=(−1)^n\arcsin a+\pi n$

b)

$𝑥=(−1)^{1+n}\arcsin a+\pi n$

c)

𝑥 = ±𝑎𝑟𝑐𝑐𝑜𝑠𝑎 + 2𝜋n

d)

𝑥 = ±(𝜋 − 𝑎𝑟𝑐𝑠𝑖𝑛𝑎) + 2𝜋n

18.

𝑡g𝑥 = a

a)

𝑥 = 𝑎𝑟𝑐c𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

b)

𝑥 = 𝑎𝑟𝑐𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

c)

𝑥 = -𝑎𝑟𝑐𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = -𝑎𝑟𝑐c𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

19.

𝑡g𝑥 = −a

a)

𝑥 = 𝑎𝑟𝑐c𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

b)

𝑥 = 𝑎𝑟𝑐𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

c)

𝑥 = -𝑎𝑟𝑐𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = -𝑎𝑟𝑐c𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

20.

c𝑡g𝑥 = −a

a)

𝑥 = 𝑎𝑟𝑐c𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

b)

𝑥 = 𝑎𝑟𝑐𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

c)

𝑥 = -𝑎𝑟𝑐𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

d)

𝑥 = $\pi$ -𝑎𝑟𝑐c𝑡g𝑎 + 𝜋𝑛, 𝑛 ∈ Z

МАТЕМАТИКА 3-АЙ 3-АПТА

Total questions: 20

Worksheet time: 10mins

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