Trigonometrik tenglamalar mavzusidan test savollari

Tenglamaning yechimini toping. \sin (2x-\frac{\pi }{2})=0

1+2\sin \frac{\pi x}{2}=0   (2<x<4) tenglamaning yechimini toping.

\frac{\vert cosx\vert }{cosx}=cos 2x-1 tenglama \lbrack \pi ;2\pi \rbrack kesmada nechta ildizga ega?

cos ^{2}x=1 tenglamaning nechta ildizi x^2\le 10 shartni qanoatlantiradi

\vert \sin 3x\vert =\frac{1}{2} tenglamani yeching.

Agar \vert cosx\vert = 2 + cosx bo‘lsa, 2^{cosx}+3^{sinx} ning qiymatini toping.

f(x)=\frac{3\sqrt{x}-4\sqrt{2-x}}{\sin (\pi x)} funksiyaning aniqlanish sohasini toping.

ctg(\frac{\pi }{2})(x-1)=0 tenglamaning (1; 5) oraliqda nechta ildizi bor?

sin (\pi cos3x)=1 tenglamani yeching

\sin (\pi cosx)=0 tenglamani yeching.

\sin (10\pi /x)=0 tenglamaning nechta butun yechimlari bor?

(8x-1)(x+2)ctg\pi x=0 tenglama [-2; 2] kesmada nechta ildizga ega?

\sin 2x=(cosx-sinx)^{2} tenglamaning [0; 2\pi ] kesmada nechta ildizi bor?

Ushbu \sin \frac{\pi }{x}=1 tenglamaning [0.05; 0.1] oraliqda nechta ildizi bor?

Ushbu sinx=\frac{2b-3}{4-b} tenglama b ning nechta butun qiymatida yechimga ega bo‘ladi?

Tenglamani yeching: tg(\frac{\pi }{2}+\frac{\sqrt{2}\pi }{4}\cdot \cos 2x)=1

Tenglamaning eng kichik musbat ildizini toping: tg\pi x^{2}=tg(\pi x^{2}+2\pi x)

Tenglamani yeching: 4\sin ^{2}2x=3

Tenglamani yeching: 2\sin 2x = -1

Tenglamani yeching: 2 sinx =-\sqrt{3}

Tenglamaning (0; 2\pi ) oraliqqa tegishli yechimlarini toping. cosx=-\frac{\sqrt{2}}{2}

Quyidagi sonlardan qaysi biri cos \frac{\pi x}{2}=1 tenglamaning ildizi emas.

cosx =\frac{\sqrt{2}}{2} tenglamaning (0;2\pi ) oraliqqa tegishli yechimlarini toping.

Tenglamani yeching: 2cosx =-\sqrt{3}

Quydagi sonlardan qaysi biri sin \frac{\pi x}{2}=1 tenglamaning ildizi emas.

Tenglamaning yechimini toping:  cos (2x-\frac{\pi }{2})=0

Tenglamani yeching:  sin (3x-\frac{\pi }{2})=0

Tenglamani yeching. 2 sinx=-1

Tenglamani yeching. tgx-tg\frac{\pi }{3}- tgx \cdot tg\frac{\pi }{3} = 1

k ning quyida ko‘rsatilgan qiymatlaridan qaysi birida coskx\cdot cos 4x- sinkx\cdot sin 4x = \frac{\sqrt{3}}{2} tenglamaning ildizlari \pm \frac{\pi }{60}+\frac{\pi }{5}n, n\in {Z} bo‘ladi?