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CBSE · Class 11 · Mathematics

Trigonometric Functions

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
60° in radians is:
  1. 2π/3
  2. π/3
  3. −π/3
  4. π/6
2.
π/3 radians in degrees is:
  1. 60°
  2. 120°
  3. 150°
  4. 61°
3.
The value of sec(−585°) is:
  1. −1/√2
  2. √2
  3. 1/2
  4. −√2
4.
An arc of a circle of radius 7 cm subtends an angle of 135° at the centre. Its length is (π = 22/7):
  1. 8.25 cm
  2. 33 cm
  3. 945 cm
  4. 16.5 cm
5.
One radian is the angle subtended at the centre of a circle by an arc whose length equals:
  1. half the radius
  2. the diameter
  3. the radius
  4. the circumference
6.
The value of cos 255° is:
  1. (4 + √2 − √6)/4
  2. (√2 − √6)/4
  3. (√6 − √2)/4
  4. −(√2 + √6)/4
7.
If cos x = 40/41 and x lies in the first quadrant, then sin x is:
  1. −41/9
  2. 9/41
  3. −9/41
  4. 41/9
8.
Assertion (A): cosec 120° = 2√3/3.
Reason (R): cosec(180° − θ) = −cosec θ.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Convert (a) 18° into radians, (b) 4π radians into degrees.
10.
In a circle of radius 42 cm, find the angle (in radians and in degrees) subtended at the centre by an arc of length 66 cm. (π = 22/7)
11.
Find the values of sin(−405°) and cosec 660°.
12.
If cos x = −8/17 and x lies in the third quadrant, find the values of the other five trigonometric functions.
13.
Find the exact value of tan 345°.
14.
If sin x = 15/17 and x lies in the first quadrant, find sin 2x, cos 2x and tan 2x.
15.
Evaluate tan2(π/6) − sin2(0) + tan2(0).
16.
The minute hand of a clock is 14 cm long. How far does its tip move in 20 minutes? (π = 22/7)
Section C — Word problems4 × 4 = 16 marks
17.
If cos x = 24/25 and x lies in the first quadrant, find (a) sin x, tan x, sec x; (b) sin 2x and cos 2x.
18.
If sin A = 12/13 and cos B = 5/13, where A and B are acute angles, find sin(A + B) and cos(A − B).
19.
Find the value of tan 960° × cos 960° + tan 660°.
20.
A wheel makes 240 revolutions in one minute. Through how many radians does it turn in one second? In 5 seconds?
AmbifulWorksheets
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CBSE · Class 11 · Mathematics

Answer key

Trigonometric Functions · AW-11M-TRF-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(b) π/3× π/180
2(a) 60°× 180/π
3(d) −√2−585° is in the second quadrant; reference angle 45°
4(d) 16.5 cml = rθ = 7 × 3π/4
5(c) the radius—
6(b) (√2 − √6)/4255° = 210° + 45°
7(b) 9/41the third side is 9; signs from the quadrant
8(c) A is true, but R is false.A is true: cosec(180° − 60°) = cosec 60° = 2√3/3. R is false.
9(a) π/10; (b) 720°180° = π radians
10π/2 radians = 90°θ = l/r = 66 ÷ 42
11−1/√2 and −2√3/3reduce each angle: −405° ≡ 315°, 660° ≡ 300°
12sin x = −15/17, tan x = 15/8, cosec x = −17/15, sec x = −17/8, cot x = 8/15the sides are 15, 8, 17; signs from the quadrant
13√3 − 2345° = 300° + 45°; use the tan(A + B) formula
14sin 2x = 240/289, cos 2x = −161/289, tan 2x = −240/161cos x = 8/17; sin 2x = 2 sin x cos x; cos 2x = cos2 x − sin2 x
151/3tan2(π/6) = 1/3, sin2(0) = 0, tan2(0) = 0
1629.33 cm20 minutes = 120° = 2π/3 radians; l = rθ
17(a) sin x = 7/25, tan x = 7/24, sec x = 25/24; (b) sin 2x = 336/625, cos 2x = 527/625sin2 x = 1 − cos2 x; sign of sin x from the quadrant
18sin(A + B) = 120/169; cos(A − B) = 1cos A = 5/13, sin B = 12/13
19−3√3/2tan 960° = √3; cos 960° = −1/2; tan 660° = −√3
208π radians per second; 40π radians in 5 secondsone revolution = 2π; 240 ÷ 60 revolutions a second