Trigonometry Practice Questions

HSC/SSC (Bangladesh) · HSC Mathematics · 115 free MCQs with instant results and detailed explanations.

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Sample Questions from Trigonometry

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Easy

If cos(θ) = 0.6, what is sin²(θ)?

A. 0.36

B. 0.64

C. 0.76

D. 0.49

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Correct Answer: B

Using the Pythagorean identity sin²(θ) + cos²(θ) = 1, we can find sin²(θ) = 1 - cos²(θ) = 1 - (0.6)² = 1 - 0.36 = 0.64.

Easy

In a right triangle, if one of the angles is 45°, what is the ratio of the length of the opposite side to the adjacent side?

A. 1:1

B. 1:2

C. 2:1

D. √2:1

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Correct Answer: A

In a 45°-45°-90° triangle, the lengths of the opposite and adjacent sides are equal, resulting in a ratio of 1:1.

Easy

If tan(x) = 1, what is the value of x in the range of 0° to 180°?

A. 45°

B. 90°

C. 135°

D. 180°

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Correct Answer: A

The tangent of an angle is equal to 1 at 45 degrees and also at 225 degrees, but 225 is outside the range of 0° to 180°.

Medium

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

A. 3/5

B. 4/5

C. 1/2

D. 1/√2

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Correct Answer: A

Using the identity tan(θ) = sin(θ)/cos(θ). If tan(θ) = 3/4, we can find the hypotenuse as 5, leading to sin(θ) = 3/5.

Medium

Which of the following is the correct formula for the sine of the sum of two angles?

A. sin(A + B) = sinA + sinB

B. sin(A + B) = sinA cosB + cosA sinB

C. sin(A + B) = cosA + cosB

D. sin(A + B) = sinA sinB

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Correct Answer: B

The sine of the sum of two angles is given by sin(A + B) = sinA cosB + cosA sinB according to trigonometric identities.

Medium

If cos(α) = 0.6, what is the value of sin²(α) + cos²(α)?

A. 1

B. 0.6

C. 0.36

D. 0.16

Show Answer & Explanation

Correct Answer: A

According to the Pythagorean identity, sin²(α) + cos²(α) = 1 for any angle α.

Medium

In a right triangle, if one angle is 45° and the length of the opposite side is 4 cm, what is the length of the hypotenuse?

A. 4√2 cm

B. 2√2 cm

C. 8 cm

D. 16 cm

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Correct Answer: A

In a 45°-45°-90° triangle, the hypotenuse is √2 times the length of each leg. Therefore, hypotenuse = 4√2 cm.

Hard

If sin(A) + sin(B) = 1 and cos(A) + cos(B) = 1, what is the value of sin(A)sin(B)?

A. 0

B. 0.5

C. 1

D. 1.5

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Correct Answer: A

The only way for sin(A) + sin(B) = 1 and cos(A) + cos(B) = 1 to hold is if one of them is 0 and the other is 1. This implies that either sin(A) = 0 or sin(B) = 0, leading to sin(A)sin(B) = 0.

Hard

In a triangle ABC, if angle A = 30 degrees and angle B = 45 degrees, find the ratio of side a to side b using the sine rule.

A. 1:√3

B. √3:1

C. 1:1

D. √2:1

Show Answer & Explanation

Correct Answer: A

Using the sine rule, a/b = sin(A)/sin(B). Here, sin(30°) = 1/2 and sin(45°) = √2/2. Thus, a/b = (1/2)/(√2/2) = 1/√2 = 1:√3 when simplified.

Q10

Hard

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

A. 4/5

B. 3/4

C. 5/3

D. 1/2

Show Answer & Explanation

Correct Answer: A

In the first quadrant, cos(A) can be found using the Pythagorean identity: sin^2(A) + cos^2(A) = 1. Here, sin(A) = 3/5, so (3/5)^2 + cos^2(A) = 1. This leads to cos(A) = 4/5.

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Trigonometry — HSC/SSC (Bangladesh) HSC Mathematics Practice Questions Online

This page contains 115 practice MCQs for the chapter Trigonometry in HSC/SSC (Bangladesh) HSC Mathematics. The questions are organized by difficulty — 26 easy, 62 medium, 27 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.