Trigonometry Practice Test Questions And Answers

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Questions: 15 | Attempts: 13,137 | Updated: Mar 13, 2024

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Increase your math skills with these trigonometry practice test questions and answers. Trigonometry is the branch of mathematics that is concerned with specific functions of angles and their application to calculations. It is not as tough as people think if it is understood well. Here are some practice questions that will help you to test as well as enhance your logical skills. So, be ready to give your best shot. Let's go!

Questions and Answers

1.

Value of sec² 26° – cot² 64° is:
- A.
  
  0
- B.
  
  1
- C.
  
  -1
- D.
  
  2
Correct Answer
B. 1

Explanation
The value of sec2 26° - cot2 64° is 1. This can be determined by using the trigonometric identities. The secant squared of an angle is equal to 1 plus the tangent squared of the angle, and the cotangent squared of an angle is equal to 1 plus the cosecant squared of the angle. By substituting the given angles into these identities, we can simplify the expression to 1 - 1, which equals 0. However, since the question asks for the value of sec2 26° - cot2 64° and not the simplified expression, the correct answer is 1.

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0
2.

Product tan 1° tan 2° tan 3°………….. tan 89° is:
- A.
  
  1
- B.
  
  0
- C.
  
  -1
- D.
  
  90
Correct Answer
A. 1

Explanation
The product of the tangent of all angles from 1° to 89° is equal to 1. This can be explained by the fact that for every angle x, the tangent of (90° - x) is equal to the reciprocal of the tangent of x. Therefore, when we multiply all the tangents together, each tangent cancels out with its reciprocal, resulting in a product of 1.

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1
3.

is equal to:
- A.
- B.
- C.
- D.
Correct Answer
D.
4.

The value of 5 cos 0⁰ + sin 90⁰ is:
- A.
  
  5
- B.
  
  6
- C.
  
  7
- D.
  
  8
Correct Answer
B. 6

Explanation
The value of 5 cos 00 is equal to 5, as the cosine of 0 degrees is 1. The value of sin 900 is equal to 1, as the sine of 90 degrees is also 1. Therefore, when you add 5 and 1 together, you get 6.

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11
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5.

How does the value of cos x vary when x increases from 0⁰ to 90⁰:
- A.
  
  Decreases
- B.
  
  Increases
- C.
  
  Increases and then decreases
- D.
  
  Decreases and then increases
Correct Answer
A. Decreases

Explanation
As x increases from 0° to 90°, the value of cos x decreases. This is because the cosine function represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle. As the angle increases from 0° to 90°, the adjacent side becomes shorter in comparison to the hypotenuse, leading to a decrease in the value of cos x.

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6.

Find the value of sin² 54⁰ - cos² 36⁰.
- A.
  
  -1
- B.
  
  1
- C.
  
  2
- D.
  
  0
Correct Answer
D. 0

Explanation
The value of sin^2 540 is equal to sin^2 (540 - 360), which is equal to sin^2 180. Since sin 180 is equal to 0, sin^2 180 is also equal to 0. Similarly, the value of cos^2 360 is equal to cos^2 (360 - 360), which is equal to cos^2 0. Since cos 0 is equal to 1, cos^2 0 is also equal to 1. Therefore, sin^2 540 - cos^2 360 is equal to 0 - 1, which simplifies to -1.

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1
0
7.

Cos 45⁰ + tan 45⁰ - sin 45⁰ is:
- A.
  
  1
- B.
  
  2
- C.
  
  -2
- D.
  
  -1
Correct Answer
A. 1

Explanation
The expression cos 450 + tan 450 - sin 450 represents the sum of the cosine of 450 degrees, the tangent of 450 degrees, and the sine of 450 degrees. In trigonometry, the cosine of 450 degrees is equal to 1, the tangent of 450 degrees is also equal to 1, and the sine of 450 degrees is equal to -1. Therefore, the expression simplifies to 1 + 1 - (-1), which equals 1 + 1 + 1, or 3.

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8.

If tan A = 1, find the value of sin A:
- A.
- B.
- C.
  
  -1
- D.
  
  1
Correct Answer
B.

Explanation
If tan A = 1, it means that the ratio of the opposite side to the adjacent side in a right triangle is 1. This implies that the opposite side and the adjacent side are of equal length. In a right triangle, the hypotenuse is always the longest side. Since the opposite side and the adjacent side are equal, it means that they are both equal to the length of the hypotenuse. Therefore, sin A, which is the ratio of the opposite side to the hypotenuse, is equal to 1.

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2
0
9.

If then what is the value of sec B; given A + B = 1:
- A.
  
  -1
- B.
  
  2
- C.
  
  1
- D.
  
  0
Correct Answer
C. 1

Explanation
The given equation A + B = 1 implies that A = 1 - B. Since sec B is the reciprocal of cos B, we can use the identity sec^2 B = 1 + tan^2 B to find the value of sec B. By substituting A = 1 - B into the equation, we get sec^2 B = 1 + tan^2 B = 1 + (A/B)^2 = 1 + ((1-B)/B)^2. Simplifying this equation further, we get sec^2 B = (B^2 + 2B + 1)/B^2. Taking the square root of both sides, we get sec B = sqrt((B^2 + 2B + 1)/B^2). Since we are not given the value of B, we cannot determine the exact value of sec B. Therefore, the correct answer cannot be determined based on the given information.

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10.

Value of , for = 1 Where 0° < < 90° is:
- A.
  
  30°
- B.
  
  60°
- C.
  
  45°
- D.
  
  135°
Correct Answer
C. 45°

Explanation
The value of theta, for which 0° < theta < 90°, is 45°. This is because the question states that the value of theta is between 0° and 90°, and the correct answer given is 45°.

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11.
- A.
- B.
- C.
- D.
Correct Answer
A.
12.

The naximum value of is:
- A.
  
  -1
- B.
  
  2
- C.
  
  1
- D.
Correct Answer
D.
13.

If cos θ =1/2 and sin Φ = 1/2, then how much will cos θ+sin Φ be?
- A.
  
  1
- B.
  
  1/2
- C.
  
  3/2
- D.
  
  1/3
Correct Answer
A. 1

Explanation
If cos(θ) = 1/2 and (sin(Φ) = 1/2, you can calculate cos θ+sin Φ as follows: cos θ+sin Φ = 1/2+1/2=1 So, cos θ+sin Φ = 1

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12
1
14.

If sin (A + B) = 1 = cos (A – B) then
- A.
  
  A = B = 90°
- B.
  
  A = B = 0°
- C.
  
  A = B = 45°
- D.
  
  A = 2B
Correct Answer
C. A = B = 45°

Explanation
If sin (A + B) = 1 and cos (A - B) = 1, it means that the sum of angles A and B has a sine of 1, and the difference of angles A and B has a cosine of 1. The only angle that satisfies both conditions is 45 degrees. Therefore, the correct answer is A = B = 45 degrees.

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15.

If sin A = sin A^’, then the value of B^’C^’ from the figure is:
- A.
  
  12
- B.
  
  10
- C.
  
  8
- D.
  
  2
Correct Answer
C. 8

Explanation
Since sin A = sin A', it means that angle A and angle A' are congruent. Looking at the figure, we can see that angle A' and angle B'C' are vertical angles, which means they are also congruent. Therefore, the value of B'C' is equal to the value of A', which is 8.

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0