Trigonometry Practice Questions

NECO (Nigeria) · NECO Mathematics · 125 free MCQs with instant results and detailed explanations.

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Sample Questions from Trigonometry

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Easy

If tan(θ) = 3/4, what is the value of sin(θ) in terms of the hypotenuse?

A. 3√(25)/25

B. 3/5

C. 4/5

D. √(25)/5

Show Answer & Explanation

Correct Answer: B

Using the definition of tangent, tan(θ) = opposite/adjacent. Here, opposite = 3 and adjacent = 4, making the hypotenuse 5. Thus, sin(θ) = opposite/hypotenuse = 3/5.

Easy

Which of the following ratios represents tan(45°)?

A. 1

B. 0

C. √3

D. √2

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Correct Answer: A

The tangent of 45 degrees is defined as 1, as the opposite and adjacent sides are equal.

Easy

If cos(θ) = 0.6, what is the value of sin(θ) if θ is in the first quadrant?

A. 0.8

B. 0.6

C. 0.5

D. 0.4

Show Answer & Explanation

Correct Answer: A

Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we find sin(θ) = √(1 - 0.6²) = √0.64 = 0.8.

Medium

If sin(x) = 0.6, what is the value of cos(x) if x is in the first quadrant?

A. 0.8

B. 0.6

C. 0.4

D. 0.3

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Correct Answer: A

In the first quadrant, cos(x) can be found using the identity sin²(x) + cos²(x) = 1. Thus, cos(x) = √(1 - sin²(x)) = √(1 - 0.36) = √0.64 = 0.8.

Medium

What is the value of tan(45° + x) in terms of tan(x)?

A. (1 + tan(x)) / (1 - tan(x))

B. 1 + tan(x)

C. tan(x)

D. 1 - tan(x)

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Correct Answer: A

The formula for tan(A + B) is tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B). Since tan(45°) = 1, we can substitute: tan(45° + x) = (1 + tan(x)) / (1 - tan(x)).

Medium

In a right triangle, if the opposite side is 5 units and the hypotenuse is 13 units, what is the value of sin(θ)?

A. 5/13

B. 12/13

C. 13/5

D. 1/2

Show Answer & Explanation

Correct Answer: A

The sine of an angle in a right triangle is given by the ratio of the length of the opposite side to the hypotenuse. Hence, sin(θ) = opposite/hypotenuse = 5/13.

Medium

Which of the following is the correct value of cos(60°)?

A. 0.5

B. 1

C. √2/2

D. √3/2

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Correct Answer: A

The cosine of 60° is a standard value in trigonometry, which is known to be 0.5.

Hard

If sin(θ) = 0.6 and θ is in the first quadrant, what is the value of cos(θ)?

A. 0.8

B. 0.75

C. 0.6

D. 0.4

Show Answer & Explanation

Correct Answer: A

Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we can find cos(θ). Here, sin²(θ) = 0.6² = 0.36. Thus, cos²(θ) = 1 - 0.36 = 0.64. Taking the square root gives cos(θ) = √0.64 = 0.8.

Hard

In triangle ABC, if angle A = 30°, angle B = 60°, and side a = 10 units, what is the length of side b using the Law of Sines?

A. 8.66 units

B. 5 units

C. 7.5 units

D. 6.89 units

Show Answer & Explanation

Correct Answer: A

Using the Law of Sines, we have a/sin(A) = b/sin(B). Here, a = 10, A = 30°, and B = 60°. Thus, b = a * (sin(B) / sin(A)) = 10 * (sin(60°) / sin(30°)) = 10 * (√3/2) / (1/2) = 10 * √3 = 8.66 units.

Q10

Hard

If sin(A) = 3/5, what is the value of cos(A) in the first quadrant?

A. 4/5

B. 3/5

C. 5/3

D. 1/2

Show Answer & Explanation

Correct Answer: A

In the first quadrant, sin²(A) + cos²(A) = 1. Given sin(A) = 3/5, we can find cos(A) using the identity. (3/5)² + cos²(A) = 1, hence cos²(A) = 1 - 9/25 = 16/25, so cos(A) = 4/5.

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Trigonometry — NECO (Nigeria) NECO Mathematics Practice Questions Online

This page contains 125 practice MCQs for the chapter Trigonometry in NECO (Nigeria) NECO Mathematics. The questions are organized by difficulty — 33 easy, 63 medium, 29 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.