Online Test — Trigonometry
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
In a right-angled triangle, if the perpendicular is 5 cm and the hypotenuse is 13 cm, what is the value of cos theta?
5/13
12/13
13/12
12/5
Explanation: Base = √(13² - 5²) = 12 cm. cos theta = Base / Hypotenuse = 12/13.
Question 2 of 10
medium
What is the exact numerical value of tan 45° + cos 60°?
1
1/2
3/2
√3
Explanation: tan 45° = 1 and cos 60° = 1/2. 1 + 1/2 = 3/2.
Question 3 of 10
medium
Simplify the expression: sin 18° / cos 72°.
0
1
-1
Not Defined
Explanation: Since 18° + 72° = 90°, sin 18° = cos 72°. The fraction equals 1.
Question 4 of 10
medium
Which of the following is equivalent to 1 - cos² theta?
cos² theta
tan² theta
sin² theta
1
Explanation: This is a direct rearrangement of the fundamental identity sin² theta + cos² theta = 1.
Question 5 of 10
medium
If sin theta = cos theta for an acute angle theta, what is the measurement of the angle?
30°
60°
0°
45°
Explanation: From the standard angle values, both sin 45° and cos 45° equal 1/√2.
Question 6 of 10
medium
Evaluate the following product: tan 30° × cot 30°.
√3
1
1/√3
0
Explanation: Tangent and cotangent are reciprocals of each other, so their product is always 1.
Question 7 of 10
medium
If cos A = 4/5, find the value of tan A.
3/4
4/3
3/5
5/3
Explanation: Perpendicular = √(5² - 4²) = 3. tan A = Perpendicular / Base = 3/4.
Question 8 of 10
medium
Simplify the expression completely: cos (90° - theta).
sec theta
cos theta
sin theta
-sin theta
Explanation: This is a direct application of the complementary angle transformation rule.
Question 9 of 10
medium
What is the value of sin² 30° + cos² 30°?
1/2
√3/2
1
2
Explanation: According to the Pythagorean identity, sin² theta + cos² theta = 1 for any angle.
Question 10 of 10
medium
If tan theta = √3, what is the value of the acute angle theta?
30°
45°
90°
60°
Explanation: According to the standard trigonometric ratios table, tan 60° = √3.