Pure Mathematics - Trigonometry Practice Questions
A-Levels · A-Level Mathematics · 122 free MCQs with instant results and detailed explanations.
122
Total
28
Easy
74
Medium
20
Hard
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Sample Questions from Pure Mathematics - Trigonometry
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Q1
Easy
If cos(ฮธ) = 0.6, what is the value of sinยฒ(ฮธ)?
A.
0.36
B.
0.64
C.
0.2
D.
0.8
Show Answer & Explanation
Correct Answer: B
Using the identity sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1, we get sinยฒ(ฮธ) = 1 - cosยฒ(ฮธ) = 1 - (0.6)ยฒ = 0.64.
Q2
Easy
Which trigonometric identity is correct?
A.
sinยฒx + cosยฒx = 1
B.
tanx = sinx/cosx
C.
secx = 1/tanx
D.
cotx + cscx = 1
Show Answer & Explanation
Correct Answer: A
The identity sinยฒx + cosยฒx = 1 is fundamental in trigonometry and holds for all values of x.
Q3
Easy
What is the value of tan(45ยฐ)?
A.
0
B.
1
C.
โ
D.
โ3
Show Answer & Explanation
Correct Answer: B
The tangent of 45 degrees is equal to 1, as it is the ratio of the opposite side to the adjacent side in a right triangle with equal sides.
Q4
Medium
What is the value of sin(30ยฐ) + cos(60ยฐ)?
A.
1
B.
0.5
C.
0.75
D.
0
Show Answer & Explanation
Correct Answer: A
Both sin(30ยฐ) and cos(60ยฐ) equal 0.5, so their sum is 0.5 + 0.5 = 1.
Q5
Medium
If tan(ฮธ) = 3/4, what is the value of sin(ฮธ) when ฮธ is in the first quadrant?
A.
3/5
B.
4/5
C.
12/13
D.
5/13
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean identity: opposite = 3, adjacent = 4. Hypotenuse = 5, thus sin(ฮธ) = opposite/hypotenuse = 3/5.
Q6
Medium
What is the exact value of cos(45ยฐ) - sin(45ยฐ)?
A.
0
B.
1
C.
โ2 - 1
D.
โ2
Show Answer & Explanation
Correct Answer: A
Both cos(45ยฐ) and sin(45ยฐ) equal โ2/2. Therefore, cos(45ยฐ) - sin(45ยฐ) = โ2/2 - โ2/2 = 0.
Q7
Medium
In a right triangle, if angle A = 30ยฐ and side opposite A is 7 cm, what is the length of the hypotenuse?
A.
14 cm
B.
7 cm
C.
7โ3 cm
D.
12 cm
Show Answer & Explanation
Correct Answer: A
Using sin(30ยฐ) = opposite/hypotenuse, we get 0.5 = 7/hypotenuse. Hence, hypotenuse = 7/0.5 = 14 cm.
Q8
Hard
If sin(ฮธ) = 3/5 for ฮธ in the first quadrant, what is the value of tan(ฮธ)?
A.
3/4
B.
4/3
C.
5/3
D.
5/4
Show Answer & Explanation
Correct Answer: B
To find tan(ฮธ), we use the identity tan(ฮธ) = sin(ฮธ)/cos(ฮธ). We know sin(ฮธ) = 3/5. Using the Pythagorean identity, cos(ฮธ) = โ(1 - sinยฒ(ฮธ)) = โ(1 - (3/5)ยฒ) = โ(1 - 9/25) = โ(16/25) = 4/5. Therefore, tan(ฮธ) = (3/5) / (4/5) = 3/4 รท 4/5 = 3/4 ร 5/4 = 15/16. Thus, tan(ฮธ) = 4/3 is correct.
Q9
Hard
The angle of elevation from a point on the ground to the top of a tower is 45 degrees. If the height of the tower is h meters, what is the horizontal distance from the point to the base of the tower?
A.
h
B.
hโ2
C.
h/โ2
D.
2h
Show Answer & Explanation
Correct Answer: A
In a right triangle where the angle of elevation is 45 degrees, the opposite and adjacent sides are equal. Thus, if the height of the tower is h, the horizontal distance from the point to the base is also h.
Q10
Hard
If sin(A) = 3/5, what is the value of tan(A) in terms of sine?
A.
3/4
B.
5/3
C.
4/3
D.
5/4
Show Answer & Explanation
Correct Answer: C
Using the identity tan(A) = sin(A) / cos(A), we need to find cos(A). From the Pythagorean identity, cos(A) = โ(1 - sinยฒ(A)) = โ(1 - (3/5)ยฒ) = โ(16/25) = 4/5. Therefore, tan(A) = (3/5) / (4/5) = 3/4.
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Pure Mathematics - Trigonometry โ A-Levels A-Level Mathematics Practice Questions Online
This page contains 122 practice MCQs for the chapter Pure Mathematics - Trigonometry in A-Levels A-Level Mathematics. The questions are organized by difficulty โ 28 easy, 74 medium, 20 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.