Trigonometric Functions — Class 11 MCQs with Answers

Trigonometric Functions — important questions & MCQs with answers (Class 11 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   sin 30° =

   A1/2B√3/2C1D0
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   Answer: 1/2

   Explanation: sin 30° = 1/2 is a standard value from the 30-60-90 triangle (opposite/hypotenuse = 1/2). Don't confuse it with cos 30° = √3/2 — sin and cos swap at complementary angles.

2. Q2 of 6Easy

   sin²θ + cos²θ =

   A2B0Csin2θD1
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   Answer: 1

   Explanation: The Pythagorean identity sin²θ + cos²θ = 1 holds for every θ, since (opposite/hyp)² + (adjacent/hyp)² = 1 by the Pythagorean theorem — it never equals 2 or sin 2θ.

3. Q3 of 6Medium

   The degree measure of 5π/6 radians is:

   A210°B120°C135°D150°
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   Answer: 150°

   Explanation: Multiplying by 180/π gives 5 × 180/6 = 150°.

4. Q4 of 6Medium

   Assertion (A): The domain of y = tan x is {x : x ∈ R and x ≠ (2n + 1)π/2, n ∈ Z}. Reason (R): The range of y = sec x is {y : y ∈ R, y ≤ –1 or y ≥ 1}.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: Both A and R are true but R is not the correct explanation of A

   Explanation: A is true because tan x = sin x/cos x is undefined where cos x = 0, that is at odd multiples of π/2. R is also true, but it describes the values taken by sec x and does not explain the domain of tan x.

5. Q5 of 6Hard

   If cos θ = −1/2 and π/2 < θ < π, sin θ =

   A√3/2B−√3/2C1/2D−1/2
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   Answer: √3/2

   Explanation: From sin²θ+cos²θ=1: sin²θ = 1 − 1/4 = 3/4, so sinθ = ±√3/2. Since π/2<θ<π places θ in the 2nd quadrant, where sine is positive, sinθ = √3/2 — dropping that sign is the standard trap.

6. Q6 of 6Hard

   Assertion (A): cos (–1710°) = 0. Reason (R): cos (–x) = –cos x for all real x.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: A is true but R is false

   Explanation: A is true: adding 5 × 360° gives cos (–1710°) = cos (–1710° + 1800°) = cos 90° = 0. R is false: cosine is even, so cos (–x) = cos x.

Trigonometric Functions notes: key concepts (Class 11 Mathematics)

This chapter frees trigonometry from right triangles, defining ratios for any angle via radian measure and the unit circle. It develops the fundamental identity, the sign rules across quadrants, compound-, multiple- and half-angle formulae, product-to-sum conversions, and the general solutions of trigonometric equations.

Radian measure

The angle a circle's centre subtends by an arc equal to the radius. π radians = 180°, so 1 rad ≈ 57.3°, and arc length l = rθ.

Signs in quadrants (ASTC)

The ASTC rule: All ratios positive in Q-I, only Sine in Q-II, only Tangent in Q-III, only Cosine in Q-IV. Fix the sign before computing.

Fundamental identities

From sin²θ+cos²θ=1 follow 1+tan²θ=sec²θ and 1+cot²θ=cosec²θ. These convert between the ratios in a single step.

Domain and range

sin and cos take all reals with range [−1,1]; tan and cot exclude points where they blow up. sec and cosec have range outside (−1,1).

Periodicity

sin, cos, sec and cosec repeat every 2π while tan and cot repeat every π. This periodicity is why equations have infinitely many solutions.

Allied angles

Ratios of −θ, 90°±θ, 180°±θ reduce to ratios of θ. Odd multiples of 90° swap sin↔cos; even multiples keep the same ratio.

Compound-angle formulae

sin(A±B)=sinA cosB±cosA sinB and cos(A±B)=cosA cosB∓sinA sinB expand sums and differences of two angles.

Tangent of a sum

tan(A±B)=(tanA±tanB)/(1∓tanA tanB). It is undefined where the denominator vanishes, matching tan's own undefined points.

Multiple-angle formulae

Double- and triple-angle results: sin2A=2sinA cosA, cos2A=cos²A−sin²A=1−2sin²A; sin3A=3sinA−4sin³A and cos3A=4cos³A−3cosA.

Half-angle formulae

With t=tan(A/2), sinA=2t/(1+t²) and cosA=(1−t²)/(1+t²). These rationalise ratios and help in integration and equations.

Product-to-sum

2sinA cosB=sin(A+B)+sin(A−B) and 2cosA cosB=cos(A+B)+cos(A−B) turn products of ratios into sums for easy simplification.

General solutions

Every root of a trig equation is captured by sinθ=sinα ⇒ θ=nπ+(−1)ⁿα; cosθ=cosα ⇒ θ=2nπ±α; tanθ=tanα ⇒ θ=nπ+α, n∈ℤ.

Standard angle values & graphs

Know sin, cos and tan at 0°, 30°, 45°, 60° and 90°; their graphs are periodic — sine and cosine have period 2π and range [−1, 1], while tan has period π and is unbounded.