Online Test — Trigonometric Functions
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
medium
tan 2A equals:
2tanA/(1−tan²A)
2tanA/(1+tan²A)
tan²A
1/tanA
Explanation: Double-angle formula.
Question 2 of 10
easy
Evaluate: sin²(π/6) + cos²(π/3) − tan²(π/4).
−1/2
1/2
0
1
Explanation: sin(π/6) = 1/2, cos(π/3) = 1/2, tan(π/4) = 1. Substituting: (1/2)² + (1/2)² − 1² = 1/4 + 1/4 − 1 = 1/2 − 1 = −1/2.
Question 3 of 10
easy
In ∆ABC, the value of a(cosB cosC + sinB sinC) evaluates to:
a
b cosC
c cosB
a cos(B−C)
Explanation: The term (cosB cosC + sinB sinC) is the trigonometric expansion for cos(B−C). Thus, the expression simply translates to a cos(B−C).
Question 4 of 10
easy
If sides are proportional to 3 : 4 : 5, then the triangle is:
Acute
Obtuse
Right
Equilateral
Explanation: 3² + 4² = 5², so it is right-angled.
Question 5 of 10
medium
If sin θ = 3/5 and θ is acute, then cos θ is:
4/5
3/4
5/4
2/5
Explanation: Using sin²θ + cos²θ =1.
Question 6 of 10
medium
Which function is even?
sin x
tan x
cot x
cos x
Explanation: cos(−x)=cosx.
Question 7 of 10
medium
Find the radius of the circle in which a central angle of 60° intercepts an arc of length 37.4 cm (use π = 22/7).
35.7 cm
37.4 cm
40.2 cm
32.5 cm
Explanation: θ = 60° = π/3 radians. Radius r = l/θ = 37.4 / (π/3) = (37.4 × 3 × 7) / 22 = 1.7 × 21 = 35.7 cm.
Question 8 of 10
medium
Find the range of the function f(x) = 3 sin(2x) − 1.
[−3, 3]
[−4, 2]
[−2, 4]
[−1, 1]
Explanation: The sine function sin(2x) has a range of [−1, 1]. Multiplying by 3 gives [−3, 3]. Subtracting 1 shifts the range to [−3−1, 3−1] = [−4, 2].
Question 9 of 10
medium
What is the general solution of cos 2x = −1/√2 (where n ∈ Z)?
nπ ± 3π/8
nπ ± 3π/4
2nπ ± 3π/8
nπ ± π/8
Explanation: cos 2x = cos(3π/4) → 2x = 2nπ ± 3π/4 → x = nπ ± 3π/8.
Question 10 of 10
easy
A Ferris wheel completes one revolution in equal intervals. If the height model gives sin θ = 1/2, which angle is a valid principal solution?
30°
210°
330°
270°
Explanation: sin θ = 1/2 at 30° and 150°. Among options only 30° works.