Trigonometry and geometry

Written by Hassan Raza (Mathematics)

8 NET Mathematics questions with answers and explanations.

Printable worksheet with answer key

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
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Correct answer: 1/2

cos 2A = 1 - 2 sin² A = 1 - 2 x 1/4 = 1/2.

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What is the exact value of tan 15 degrees?
- 1 sqrt(3) - 2
- 2 2 - sqrt(3)
- 3 1 / sqrt(3)
- 4 2 + sqrt(3)
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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).

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

cos A = (b² + c² - a²) / 2bc = (64 + 81 - 49) / 144 = 96 / 144 = 2/3.

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

Area = 1/2 r² theta = 1/2 x 36 x pi/3 = 6 pi.

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What is the period of sin 3x?
- 1 pi
- 2 6 pi
- 3 2 pi
- 4 2 pi / 3
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Correct answer: 2 pi / 3

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

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What is the value of the inverse sine of 1, in radians?
- 1 0
- 2 pi / 2
- 3 pi / 4
- 4 pi
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Correct answer: pi / 2

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

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How many solutions does sin x = 0 have in the closed interval from 0 to 2 pi?
- 1 1
- 2 4
- 3 2
- 4 3
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Correct answer: 3

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

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What is the distance from the origin to the line 3x + 4y - 10 = 0?
- 1 2
- 2 1
- 3 10
- 4 5
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Correct answer: 2

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

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