Trigonometry Practice Questions
Thanaweya Amma (Egypt) · Thanaweya Mathematics · 127 free MCQs with instant results and detailed explanations.
127
Total
31
Easy
70
Medium
26
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
What is the sine of a 30-degree angle?
A.
0.5
B.
0.866
C.
1
D.
0
Show Answer & Explanation
Correct Answer: A
The sine of 30 degrees is 0.5, which can be derived from the properties of a right triangle where the opposite side is half the hypotenuse.
Q2
Easy
In a right triangle, if the opposite side is 3 units and the hypotenuse is 5 units, what is the cosine of the angle opposite the 3-unit side?
A.
0.6
B.
0.8
C.
0.5
D.
0.7
Show Answer & Explanation
Correct Answer: B
Cosine is defined as the adjacent side over the hypotenuse. The adjacent side can be calculated using the Pythagorean theorem, yielding cos(ฮธ) = 4/5 = 0.8.
Q3
Easy
Which of the following is the correct relationship in trigonometry for a right triangle?
A.
cosยฒ(ฮธ) + sinยฒ(ฮธ) = 1
B.
sin(ฮธ) + cos(ฮธ) = 1
C.
tan(ฮธ) = sin(ฮธ)/cos(ฮธ)
D.
All of the above
Show Answer & Explanation
Correct Answer: D
All options represent valid relationships in trigonometry: the Pythagorean identity, sine and cosine value addition, and the definition of tangent.
Q4
Medium
Given a right triangle where angle A = 30ยฐ and the length of the opposite side to angle A is 5 cm, what is the length of the hypotenuse?
A.
10 cm
B.
5โ3 cm
C.
5 cm
D.
15 cm
Show Answer & Explanation
Correct Answer: A
In a right triangle with angle A = 30ยฐ, the relationship between the opposite side and the hypotenuse is given by sin(30ยฐ) = opposite/hypotenuse. Therefore, hypotenuse = opposite/sin(30ยฐ) = 5/sin(30ยฐ) = 5/(1/2) = 10 cm.
Q5
Medium
If tan(ฮธ) = 3/4, which of the following is equal to sin(ฮธ)?
A.
3/5
B.
4/5
C.
5/4
D.
7/25
Show Answer & Explanation
Correct Answer: A
Using the definition of tangent, tan(ฮธ) = opposite/adjacent, we let opposite = 3 and adjacent = 4. The hypotenuse can be calculated using Pythagoras' theorem: hypotenuse = โ(3ยฒ + 4ยฒ) = 5. Thus, sin(ฮธ) = opposite/hypotenuse = 3/5.
Q6
Medium
If a point P on the unit circle corresponds to an angle of 120ยฐ, what are the coordinates of P?
A.
(-0.5, โ3/2)
B.
(0.5, โ3/2)
C.
(-โ3/2, -0.5)
D.
(โ3/2, -0.5)
Show Answer & Explanation
Correct Answer: A
The coordinates of a point on the unit circle at an angle of 120ยฐ can be derived from the cosine and sine values. Cos(120ยฐ) = -0.5 and Sin(120ยฐ) = โ3/2, thus the coordinates are (-0.5, โ3/2).
Q7
Medium
What is the value of cos(90ยฐ - ฮธ)?
A.
sin(ฮธ)
B.
cos(ฮธ)
C.
tan(ฮธ)
D.
tan(90ยฐ - ฮธ)
Show Answer & Explanation
Correct Answer: A
According to the co-function identity in trigonometry, cos(90ยฐ - ฮธ) is equal to sin(ฮธ). Thus, option A is correct.
Q8
Hard
What is the value of sin(ฮธ) if tan(ฮธ) = 3/4 and ฮธ is in the first quadrant?
A.
3/5
B.
4/5
C.
5/3
D.
4/3
Show Answer & Explanation
Correct Answer: A
In the first quadrant, where sin(ฮธ) can be determined using the relationship between tan(ฮธ) and sin(ฮธ). Given tan(ฮธ) = 3/4, we set opposite = 3 and adjacent = 4. Using the Pythagorean theorem, the hypotenuse = โ(3ยฒ + 4ยฒ) = 5. Thus, sin(ฮธ) = opposite/hypotenuse = 3/5.
Q9
Hard
If cos(ฮฑ) = 0.6, what is the value of sec(ฮฑ) and how it relates to cos(ฮฑ)?
A.
1.6
B.
0.6
C.
0.5
D.
1.6667
Show Answer & Explanation
Correct Answer: D
Secant is the reciprocal of cosine. Therefore, if cos(ฮฑ) = 0.6, sec(ฮฑ) = 1/cos(ฮฑ) = 1/0.6 = 1.6667. This establishes how sec(ฮฑ) directly relates to cos(ฮฑ).
Q10
Hard
If tan(ฮธ) = 3/4 and ฮธ is in the first quadrant, what is the value of sin(ฮธ)?
A.
3/5
B.
4/5
C.
5/9
D.
7/9
Show Answer & Explanation
Correct Answer: A
Using the definition of tangent, tan(ฮธ) = opposite/adjacent = 3/4. By the Pythagorean theorem, hypotenuse = โ(3ยฒ + 4ยฒ) = 5. Thus, sin(ฮธ) = opposite/hypotenuse = 3/5.
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Trigonometry โ Thanaweya Amma (Egypt) Thanaweya Mathematics Practice Questions Online
This page contains 127 practice MCQs for the chapter Trigonometry in Thanaweya Amma (Egypt) Thanaweya Mathematics. The questions are organized by difficulty โ 31 easy, 70 medium, 26 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.