Trigonometry and geometry

8 NET Mathematics questions with answers and explanations.

All questions with answers

If sin A = 1/2, what is cos 2A?
- 1 1/2
- 2 1/4
- 3 -1/2
- 4 sqrt(3)/2
Show answer

Correct answer: 1/2

cos 2A = 1 - 2 sin^2 A = 1 - 2 x 1/4 = 1/2.

Report a mistake
What is the exact value of tan 15 degrees?
- 1 2 + sqrt(3)
- 2 sqrt(3) - 2
- 3 2 - sqrt(3)
- 4 1 / sqrt(3)
Show answer

Correct answer: 2 - sqrt(3)

tan(45 - 30) = (1 - 1/sqrt(3)) / (1 + 1/sqrt(3)) = (sqrt(3) - 1) / (sqrt(3) + 1), which simplifies to 2 - sqrt(3).

Report a mistake
A triangle has sides a = 7, b = 8 and c = 9. What is cos A, where A is the angle opposite side a?
- 1 2/3
- 2 1/3
- 3 3/4
- 4 1/2
Show answer

Correct answer: 2/3

cos A = (b^2 + c^2 - a^2) / 2bc = (64 + 81 - 49) / 144 = 96 / 144 = 2/3.

Report a mistake
What is the area of a sector of a circle of radius 6 with a central angle of pi/3 radians?
- 1 3 pi
- 2 6 pi
- 3 12 pi
- 4 36 pi
Show answer

Correct answer: 6 pi

Area = 1/2 r^2 theta = 1/2 x 36 x pi/3 = 6 pi.

Report a mistake
What is the period of sin 3x?
- 1 2 pi
- 2 pi
- 3 2 pi / 3
- 4 6 pi
Show answer

Correct answer: 2 pi / 3

The period of sin(kx) is 2 pi / k, so here it is 2 pi / 3.

Report a mistake
What is the value of the inverse sine of 1, in radians?
- 1 0
- 2 pi / 2
- 3 pi
- 4 pi / 4
Show answer

Correct answer: pi / 2

sin(pi/2) = 1, so the inverse sine of 1 is pi/2.

Report a mistake
How many solutions does sin x = 0 have in the closed interval from 0 to 2 pi?
- 1 2
- 2 1
- 3 4
- 4 3
Show answer

Correct answer: 3

The solutions are x = 0, pi and 2 pi.

Report a mistake
What is the distance from the origin to the line 3x + 4y - 10 = 0?
- 1 2
- 2 10
- 3 5
- 4 1
Show answer

Correct answer: 2

Distance = |-10| / sqrt(9 + 16) = 10 / 5 = 2.

Report a mistake