Ba'zi trigonometrik tenglamalarni yechish usullari — 10-sinf Algebra test savollari

1.sin2x=sinx tenglamani yeching (2sinx cosx-sinx=0 ko'rinishida ko'paytuvchilarga ajratib).

• A)x=πn yoki x=±$\frac{\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• B)x=πn, n$\in$$\mathbb{Z}$
• C)$x=\frac{\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• D)$x=\frac{\pi }{2}+\pi n,n$$\in$$\mathbb{Z}$

2.sinx+cosx=0 tenglamani yeching (ikkala tomonni cosx≠0 ga bo'lib).

• A)$x=-\frac{\pi }{4}+\pi n,n$$\in$$\mathbb{Z}$
• B)$x=\frac{\pi }{4}+\pi n,n$$\in$$\mathbb{Z}$
• C)$x=\frac{\pi }{4}+2\pi n,n$$\in$$\mathbb{Z}$
• D)x=πn, n$\in$$\mathbb{Z}$

3.2sin²x-3cosx=0 tenglamani yeching (sin²x=1-cos²x almashtirib, 2cos²x+3cosx-2=0 hosil bo'ladi).

• A)x=±$\frac{\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• B)x=±$\frac{\pi }{6}+2\pi n,n$$\in$$\mathbb{Z}$
• C)$x=\frac{\pi }{2}+\pi n,n$$\in$$\mathbb{Z}$
• D)yechimi yo'q

4.cos2x=cosx tenglamani yeching (2cos²x-1-cosx=0 ko'rinishiga keltirib, t=cosx: 2t²-t-1=0 → t=1 yoki $t=-\frac{1}{2}$).

• A)x=2πn yoki x=±$\frac{2\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• B)x=πn, n$\in$$\mathbb{Z}$
• C)x=±$\frac{\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• D)yechimi yo'q

5.sinx·cosx=0 tenglamani yeching.

• A)x=πn/2, n$\in$$\mathbb{Z}$
• B)x=πn, n$\in$$\mathbb{Z}$
• C)$x=\frac{\pi }{2}+\pi n,n$$\in$$\mathbb{Z}$
• D)$x=\frac{\pi }{4}+\pi n,n$$\in$$\mathbb{Z}$

6.Bir xil darajali (odnorodniy) trigonometrik tenglamalarni yechishda odatda qanday usul qo'llaniladi?

• A)tenglamani ${\cos }^n$ x (yoki ${\sin }^n$ x) ga bo'lib, tg x ga nisbatan tenglama hosil qilish
• B)faqat kvadratga oshirish
• C)faqat logaritmlash
• D)faqat grafik usul

7.sin²x+cos²x=1 ayniyatidan sin²x ni cos²x orqali qanday ifodalash mumkin?

• A)sin²x=1-cos²x
• B)sin²x=1+cos²x
• C)sin²x=cos²x-1
• D)sin²x=cos²x

8.Ko'paytuvchilarga ajratish usulida A·B=0 tenglama qanday yechiladi?

• A)A=0 yoki B=0 tenglamalar alohida yechiladi
• B)A=B tenglama yechiladi
• C)faqat A=0 yechiladi
• D)faqat B=0 yechiladi

9.sinx=cosx tenglamani yeching.

• A)$x=\frac{\pi }{4}+\pi n,n$$\in$$\mathbb{Z}$
• B)$x=\frac{\pi }{4}+2\pi n,n$$\in$$\mathbb{Z}$
• C)x=πn, n$\in$$\mathbb{Z}$
• D)$x=\frac{\pi }{2}+\pi n,n$$\in$$\mathbb{Z}$

10.sinx(2cosx-1)=0 tenglamani yeching.

• A)x=πn yoki x=±$\frac{\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• B)x=πn, n$\in$$\mathbb{Z}$
• C)x=±$\frac{\pi }{3}+2\pi n,n$$\in$$\mathbb{Z}$
• D)yechimi yo'q