Trigonometry MCQs with Answers: ECAT Mathematics

All questions with answers

What is the value of sin 30 degrees + cos 60 degrees?
- 1 1/2
- 2 1
- 3 sqrt(3)/2
- 4 sqrt(3)
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Correct answer: 1

Both sin 30 and cos 60 equal 1/2, so the sum is 1.

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If sin A = 3/5 and A is acute, what is cos A?
- 1 3/4
- 2 5/3
- 3 4/5
- 4 2/5
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Correct answer: 4/5

cos A = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.

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If sin A = 3/5 and cos A = 4/5, what is sin 2A?
- 1 12/25
- 2 24/25
- 3 7/25
- 4 1
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Correct answer: 24/25

sin 2A = 2 sin A cos A = 2 x (3/5) x (4/5) = 24/25.

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

The tangent function repeats every pi radians.

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What is the value of cos 60 degrees + cos 120 degrees?
- 1 1
- 2 -1
- 3 1/2
- 4 0
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Correct answer: 0

cos 60 = 1/2 and cos 120 = -1/2, so the sum is 0.

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

The solutions are x = pi/6 and x = 5 pi/6.

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A triangle has sides 3, 4 and 5. What is the angle opposite the side of length 5?
- 1 60 degrees
- 2 45 degrees
- 3 90 degrees
- 4 120 degrees
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Correct answer: 90 degrees

Since 3^2 + 4^2 = 5^2, the triangle is right-angled and the angle opposite the longest side is 90 degrees.

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What is the area of a triangle with sides 7 and 8 and an included angle of 30 degrees?
- 1 28
- 2 14
- 3 56
- 4 7 sqrt(3)
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Correct answer: 14

Area = 1/2 x 7 x 8 x sin 30 = 28 x 1/2 = 14.

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Which expression equals cos(A + B)?
- 1 cos A cos B + sin A sin B
- 2 sin A cos B + cos A sin B
- 3 cos A cos B - sin A sin B
- 4 sin A sin B - cos A cos B
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Correct answer: cos A cos B - sin A sin B

The addition formula is cos(A + B) = cos A cos B - sin A sin B.

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