مثلثیات اور جیومیٹری

Written by Hassan Raza (Mathematics)

نیٹ · ریاضی · 8 سوالات

نام: ____________________ تاریخ: ____________

If sin A = 1/2, what is cos 2A?
- A -1/2
- B 1/4
- C 1/2
- D sqrt(3)/2
What is the exact value of tan 15 degrees?
- A sqrt(3) - 2
- B 2 - sqrt(3)
- C 1 / sqrt(3)
- D 2 + sqrt(3)
A triangle has sides a = 7, b = 8 and c = 9. What is cos A, where A is the angle opposite side a?
- A 1/2
- B 2/3
- C 1/3
- D 3/4
What is the area of a sector of a circle of radius 6 with a central angle of pi/3 radians?
- A 12 pi
- B 36 pi
- C 6 pi
- D 3 pi
What is the period of sin 3x?
- A pi
- B 6 pi
- C 2 pi
- D 2 pi / 3
What is the value of the inverse sine of 1, in radians?
- A 0
- B pi / 2
- C pi / 4
- D pi
How many solutions does sin x = 0 have in the closed interval from 0 to 2 pi?
- A 1
- B 4
- C 2
- D 3
What is the distance from the origin to the line 3x + 4y - 10 = 0?
- A 2
- B 1
- C 10
- D 5

جوابی کلید

1. C, 2. B, 3. B, 4. C, 5. D, 6. B, 7. D, 8. A

cos 2A = 1 - 2 sin² A = 1 - 2 x 1/4 = 1/2.
tan(45 - 30) = (1 - 1/sqrt(3)) / (1 + 1/sqrt(3)) = (sqrt(3) - 1) / (sqrt(3) + 1), which simplifies to 2 - sqrt(3).
cos A = (b² + c² - a²) / 2bc = (64 + 81 - 49) / 144 = 96 / 144 = 2/3.
Area = 1/2 r² theta = 1/2 x 36 x pi/3 = 6 pi.
The period of sin(kx) is 2 pi / k, so here it is 2 pi / 3.
sin(pi/2) = 1, so the inverse sine of 1 is pi/2.
The solutions are x = 0, pi and 2 pi.
Distance = |-10| / sqrt(9 + 16) = 10 / 5 = 2.