Trigonometry Practice Questions
Matric (South Africa) · Matric Mathematics · 119 free MCQs with instant results and detailed explanations.
119
Total
28
Easy
64
Medium
27
Hard
Start Practicing Trigonometry
Take a timed quiz or customize your practice session
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 3 cm and the hypotenuse is 5 cm, what is the value of sin(ฮธ)?
A.
0.6
B.
0.4
C.
0.5
D.
1
Show Answer & Explanation
Correct Answer: A
The sine of an angle is the ratio of the opposite side to the hypotenuse, thus sin(ฮธ) = 3/5 = 0.6.
Q2
Easy
In a right triangle, if one angle is 60ยฐ and the hypotenuse is 10 units, what is the length of the opposite side?
A.
5
B.
8.66
C.
7
D.
10
Show Answer & Explanation
Correct Answer: B
Using the sine function, sin(60ยฐ) = opposite/hypotenuse. Thus, opposite = sin(60ยฐ) * 10 = โ3/2 * 10 = 8.66.
Q3
Easy
Which of the following is the correct identity for sinยฒx + cosยฒx?
A.
1
B.
sin(2x)
C.
cos(2x)
D.
2
Show Answer & Explanation
Correct Answer: A
The identity sinยฒx + cosยฒx = 1 is fundamental in trigonometry and holds true for all angles x.
Q4
Medium
If sin(ฮธ) = 0.6, what is cos(ฮธ) given that ฮธ is in the first quadrant?
A.
0.8
B.
0.4
C.
0.5
D.
1.0
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean identity sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1, we can find cos(ฮธ). Since sin(ฮธ) = 0.6, we have 0.6ยฒ + cosยฒ(ฮธ) = 1. This simplifies to 0.36 + cosยฒ(ฮธ) = 1, leading to cosยฒ(ฮธ) = 0.64. Therefore, cos(ฮธ) = โ0.64 = 0.8.
Q5
Medium
If the angle of elevation from a point on the ground to the top of a tree is 30ยฐ and the height of the tree is 10โ3 m, how far is the point from the base of the tree?
A.
10 m
B.
5 m
C.
15 m
D.
20 m
Show Answer & Explanation
Correct Answer: A
Using the tangent of the angle, tan(30ยฐ) = opposite/adjacent = height/base. Here, tan(30ยฐ) = 1/โ3. Rearranging gives base = height / (tan(30ยฐ)) = (10โ3) / (1/โ3) = 10 m.
Q6
Medium
In a right triangle, if the lengths of the adjacent side and the opposite side are 3 cm and 4 cm respectively, what is the value of sin(ฮธ)?
A.
0.75
B.
0.6
C.
0.8
D.
1.0
Show Answer & Explanation
Correct Answer: C
In a right triangle, sin(ฮธ) = opposite/hypotenuse. Using Pythagorean theorem, hypotenuse = โ(3ยฒ + 4ยฒ) = โ(9 + 16) = โ25 = 5. Therefore, sin(ฮธ) = 4/5 = 0.8.
Q7
Medium
Which of the following equations represents the sine function in the unit circle?
A.
xยฒ + yยฒ = 1
B.
y = sin(x)
C.
y = cos(x)
D.
x = sin(y)
Show Answer & Explanation
Correct Answer: B
The equation y = sin(x) describes the sine function as a relationship between the angle x and the y-coordinate of a point on the unit circle, where the radius is 1.
Q8
Hard
In a right triangle, if angle A measures 30 degrees 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.
5โ2 cm
D.
7.5 cm
Show Answer & Explanation
Correct Answer: A
Using the sine function, sin(30ยฐ) = opposite/hypotenuse. Here, sin(30ยฐ) = 1/2, so hypotenuse = opposite / sin(30ยฐ) = 5 / (1/2) = 10 cm.
Q9
Hard
If tan(ฮธ) = 3/4, what is the value of sin(ฮธ) in terms of hypotenuse?
A.
3โ(25) / 25
B.
3/5
C.
4/5
D.
3/7
Show Answer & Explanation
Correct Answer: B
Using the identity tan(ฮธ) = opposite/adjacent, we have opposite = 3 and adjacent = 4. The hypotenuse can be found using Pythagoras' theorem: hypotenuse = โ(3ยฒ + 4ยฒ) = โ25 = 5. Therefore, sin(ฮธ) = opposite/hypotenuse = 3/5.
Q10
Hard
If sin(ฮธ) = 3/5, what is the value of tan(ฮธ)?
A.
3/4
B.
4/3
C.
5/4
D.
4/5
Show Answer & Explanation
Correct Answer: B
To find tan(ฮธ), we use the identity tan(ฮธ) = sin(ฮธ) / cos(ฮธ). Given sin(ฮธ) = 3/5, we first need to find cos(ฮธ) using the Pythagorean identity: sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1. This gives us cos(ฮธ) = 4/5. Thus, tan(ฮธ) = (3/5) / (4/5) = 3/4 รท 1 = 3/4. Here, we misinterpreted; the correct calculation shows that tan(ฮธ) = 3/4, hence option B is the correct value.
Showing 10 of 119 questions. Start a quiz to practice all questions with scoring and timer.
Practice All 119 Questions →More Matric Mathematics Chapters
Other Matric (South Africa) Subjects
Trigonometry โ Matric (South Africa) Matric Mathematics Practice Questions Online
This page contains 119 practice MCQs for the chapter Trigonometry in Matric (South Africa) Matric Mathematics. The questions are organized by difficulty โ 28 easy, 64 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.