Trigonometriya asoslari

Question 1

Chizmada tasvirlangan $\alpha$ burchak uchun quyidagi tengsizliklardan qaysi biri o‘rinli?

Accepted Answer

$\sin\alpha\cdot\cos\alpha<0$

Answer

$\mathrm{tg}\,\alpha\cdot\sin\alpha>0$

Answer

$\mathrm{ctg}\,\alpha\cdot\cos\alpha<0$

Answer

$\mathrm{ctg}\,\alpha\cdot\sin\alpha>0$

Question 2

Chizmada berilgan ma’lumotlardan foydalanib, $	ext{tg}\,\alpha$ ning qiymatini toping.

Accepted Answer

$\frac{4}{3}$

Answer

$\frac{3}{4}$

Answer

$\frac{4}{5}$

Answer

$\frac{3}{5}$

Question 3

$\cos x+\left(2+\sqrt{2}\right)\cdot\sin^2x=1$ tenglamaning $[0;\ 2\pi]$ kesmadagi yechimlari yig‘indisini toping.

Accepted Answer

$4\pi$

Answer

$\frac{7\pi}{2}$

Answer

$\frac{5\pi}{2}$

Answer

$3\pi$

Question 4

Soddalashtiring: $\frac{\cos3\alpha+\cos\alpha}{\sin3\alpha-\sin\alpha}$

Accepted Answer

$\mathrm{ctg}\,\alpha$

Answer

$\mathrm{tg}\,\alpha$

Answer

$2\,\mathrm{ctg}\,\alpha$

Answer

$2\,\mathrm{tg}\,\alpha$

Question 5

$2\cdot\left(\sin^4\frac{\pi}{8}+\cos^4\frac{3\pi}{8}+\sin^4\frac{5\pi}{8}+\cos^4\frac{7\pi}{8}\right)$ ni hisoblang.

Accepted Answer

3

Answer

3,5

Answer

2

Answer

1

Question 6

Agar $\mathrm{tg}\,\alpha+\mathrm{ctg}\,\alpha=3$ bo‘lsa, $\mathrm{tg}^2\alpha-2\mathrm{tg}\,\alpha+\mathrm{ctg}\,\alpha$ ifodaning qiymatini toping.

Accepted Answer

2

Answer

4

Answer

1

Answer

3

Question 7

Tenglamani yeching: $\frac{5}{\sin^2 x}+\frac{7}{\sin x}-6=0$

Accepted Answer

$(-1)^{k+1}\frac{\pi}{6}+\pi k, k \in Z$

Answer

$(-1)^{k}\frac{\pi}{6}+\pi k, k \in Z$

Answer

$(-1)^{k}\frac{\pi}{6}+2\pi k, k \in Z$

Answer

$\frac{\pi}{6}+2\pi k, k \in Z$

Boshqa mavzular