Trigonometry Practice Questions
SPM (Malaysia) · SPM Mathematics · 120 free MCQs with instant results and detailed explanations.
120
Total
27
Easy
66
Medium
27
Hard
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Sample Questions from Trigonometry
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
In a right triangle, if the opposite side is 4 cm and the hypotenuse is 5 cm, what is the value of sin(ฮธ)?
A.
0.8
B.
0.6
C.
0.5
D.
1
Show Answer & Explanation
Correct Answer: A
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(ฮธ) = 4/5 = 0.8.
Q2
Easy
Which of the following identities correctly represents the Pythagorean identity involving sine and cosine?
A.
sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1
B.
sin(ฮธ) + cos(ฮธ) = 1
C.
sinยฒ(ฮธ) - cosยฒ(ฮธ) = 1
D.
sin(ฮธ) * cos(ฮธ) = 1
Show Answer & Explanation
Correct Answer: A
The Pythagorean identity states that the square of sine plus the square of cosine equals one, which is fundamental in trigonometry.
Q3
Easy
In a right triangle, if the opposite side is 4 cm and the hypotenuse is 5 cm, what is the value of sin(ฮธ)?
A.
0.8
B.
0.6
C.
1.25
D.
0.4
Show Answer & Explanation
Correct Answer: A
Sin(ฮธ) is defined as the opposite side over the hypotenuse, so sin(ฮธ) = 4 cm / 5 cm = 0.8.
Q4
Medium
If sin(A) = 3/5, what is the value of cos(A)?
A.
4/5
B.
3/5
C.
5/3
D.
1/5
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean identity, cos(A) = sqrt(1 - sin^2(A)). Here, cos(A) = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.
Q5
Medium
Which of the following equations represents the tangent of an angle in a right triangle?
A.
Opposite/Adjacent
B.
Adjacent/Hypotenuse
C.
Opposite/Hypotenuse
D.
Hypotenuse/Adjacent
Show Answer & Explanation
Correct Answer: A
Tangent is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle.
Q6
Medium
What is the value of sin(60ยฐ) in exact terms?
A.
โ3/2
B.
1/2
C.
โ2/2
D.
โ5/2
Show Answer & Explanation
Correct Answer: A
The exact value of sin(60ยฐ) is โ3/2, as derived from standard trigonometric values for angles in a 30-60-90 triangle.
Q7
Medium
If sin(ฮธ) = 3/5, what is the value of cos(ฮธ) if ฮธ is in the first quadrant?
A.
4/5
B.
3/5
C.
5/3
D.
2/5
Show Answer & Explanation
Correct Answer: A
In the first quadrant, both sine and cosine are positive. Using the Pythagorean identity, we know that sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1. Thus, (3/5)ยฒ + cosยฒ(ฮธ) = 1, leading to cosยฒ(ฮธ) = 1 - 9/25 = 16/25. Therefore, cos(ฮธ) = โ(16/25) = 4/5.
Q8
Hard
If sin(ฮธ) = 0.6, what is the value of cosยฒ(ฮธ)?
A.
0.36
B.
0.64
C.
0.16
D.
0.44
Show Answer & Explanation
Correct Answer: B
Using the Pythagorean identity sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1, we can find cosยฒ(ฮธ). Since sin(ฮธ) = 0.6, we have sinยฒ(ฮธ) = 0.36. Therefore, cosยฒ(ฮธ) = 1 - sinยฒ(ฮธ) = 1 - 0.36 = 0.64, making option B the correct answer.
Q9
Hard
In a right triangle, if the angle A is 30ยฐ and the side opposite to angle A is 5 cm, what is the length of the hypotenuse?
A.
10 cm
B.
5โ3 cm
C.
5 cm
D.
10โ3 cm
Show Answer & Explanation
Correct Answer: A
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse. Therefore, sin(30ยฐ) = opposite/hypotenuse. Here, sin(30ยฐ) = 0.5. Setting up the equation 0.5 = 5/hypotenuse gives hypotenuse = 5/0.5 = 10 cm, confirming that option A is correct.
Q10
Hard
A ladder is leaning against a wall such that the angle between the ladder and the ground is 60 degrees. If the base of the ladder is 4 meters away from the wall, what is the length of the ladder?
A.
4 m
B.
8 m
C.
6 m
D.
10 m
Show Answer & Explanation
Correct Answer: B
Using the cosine ratio, we have cos(60ยฐ) = adjacent/hypotenuse. Here, adjacent = 4 m (distance from the wall). Thus, hypotenuse (ladder length) = 4/cos(60ยฐ) = 4/(1/2) = 8 m.
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Trigonometry โ SPM (Malaysia) SPM Mathematics Practice Questions Online
This page contains 120 practice MCQs for the chapter Trigonometry in SPM (Malaysia) SPM Mathematics. The questions are organized by difficulty โ 27 easy, 66 medium, 27 hard โ 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.