Trigonometry Practice Questions

WAEC (West Africa) · WAEC Mathematics · 129 free MCQs with instant results and detailed explanations.

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Sample Questions from Trigonometry

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Easy

If cos(θ) = 0.8, what is sin(θ) assuming θ is in the first quadrant?

A. 0.6

B. 0.8

C. 0.4

D. 0.9

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Correct Answer: A

Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we can find sin(θ). Substituting cos(θ) = 0.8 into the equation gives us sin²(θ) = 1 - (0.8)² = 1 - 0.64 = 0.36, so sin(θ) = √0.36 = 0.6.

Easy

If cos(θ) = 0.5, what is θ in degrees?

A. 30°

B. 60°

C. 45°

D. 90°

Show Answer & Explanation

Correct Answer: A

The cosine of 30 degrees is 0.5, making θ = 30° the correct answer.

Easy

Which of the following is the tangent of 45°?

A. 1

B. 0

C. √3

D. √3/3

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Correct Answer: A

The tangent of 45 degrees is defined as 1, as it is the ratio of the opposite side to the adjacent side, which are equal at this angle.

Medium

In a right triangle, if one angle is 30 degrees and the opposite side to this angle is 5 cm, what is the length of the hypotenuse?

A. 10 cm

B. 5 cm

C. 7.5 cm

D. 8.66 cm

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Correct Answer: A

In a right triangle with a 30-degree angle, the hypotenuse is double the length of the opposite side. Therefore, if the opposite side is 5 cm, the hypotenuse is 5 cm x 2 = 10 cm.

Medium

If sin(x) = 0.5, what is the value of x in degrees within the range of 0° to 360°?

A. 30°

B. 150°

C. 210°

D. 330°

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Correct Answer: A

The sine function reaches a value of 0.5 at angles of 30° and 150° in the first and second quadrants respectively. However, the standard answer within the primary range is 30°.

Medium

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

A. 0.8

B. 0.64

C. 0.5

D. 0.76

Show Answer & Explanation

Correct Answer: A

Using the Pythagorean identity, cos^2(x) + sin^2(x) = 1. Thus, cos^2(x) = 1 - (0.6)^2 = 0.64, and cos(x) = √0.64 = 0.8 in the first quadrant.

Medium

In a right triangle, if the angle A is 30 degrees and the hypotenuse is 10 cm, what is the length of the opposite side?

A. 5 cm

B. 10 cm

C. 15 cm

D. 8.66 cm

Show Answer & Explanation

Correct Answer: A

Using the sine function, sin(30°) = opposite/hypotenuse. Therefore, opposite = hypotenuse * sin(30°) = 10 * 0.5 = 5 cm.

Hard

In a right triangle, if one of the angles is 30 degrees and the length of the hypotenuse is 10 cm, what is the length of the side opposite to the 30-degree angle?

A. 5 cm

B. 10 cm

C. 15 cm

D. 8.66 cm

Show Answer & Explanation

Correct Answer: A

In a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse. Thus, 10 cm / 2 = 5 cm.

Hard

If sin(θ) = 0.6, what is the value of cos(θ) using the Pythagorean identity?

A. 0.8

B. 0.36

C. 0.6

D. 0.4

Show Answer & Explanation

Correct Answer: A

Using the Pythagorean identity, we know that sin²(θ) + cos²(θ) = 1. Thus, cos²(θ) = 1 - sin²(θ) = 1 - 0.36 = 0.64, and cos(θ) = √0.64 = 0.8.

Q10

Hard

If sin(θ) = 3/5, what is the value of cos(θ) in its simplest radical form?

A. 4/5

B. 3/5

C. 5/4

D. 1/5

Show Answer & Explanation

Correct Answer: A

Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we can find cos(θ). Since sin(θ) = 3/5, we have (3/5)² + cos²(θ) = 1. This simplifies to 9/25 + cos²(θ) = 1, which leads to cos²(θ) = 16/25. Taking the square root gives cos(θ) = 4/5.

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Trigonometry — WAEC (West Africa) WAEC Mathematics Practice Questions Online

This page contains 129 practice MCQs for the chapter Trigonometry in WAEC (West Africa) WAEC Mathematics. The questions are organized by difficulty — 31 easy, 66 medium, 32 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.