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Saturday, 10 October

JEE Main Maths · Class 11

Trigonometric Functions: JEE Main previous year questions

Trigonometric Functions had 41 questions in the 42 JEE Main shifts Lumi analysed, about 1.0 a shift, asked in 31 of 42 shifts. It ranks 16 of 22 Maths chapters by questions; 17% of its questions were hard.

Questions
41
in 31 of 42 shifts
A shift, on average
1.0
of 25 Maths questions
Since 2024
-0.1
1.0 a shift in 2017–23, 0.9 in 2024–26
Numerical answer
11
27% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
06122’171’206’215’223’237’246’2511’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20172
  • 20201
  • 20216
  • 20225
  • 20233
  • 20247
  • 20256
  • 202611
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

6 topics and 23 distinct ideas; 3 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

10 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
3 repeat

Study it on Lumi

Trigonometric Functions: the interactive lesson

Every question

All 41 Trigonometric Functions questions

Newest first. Each opens with its options and the official answer.

2026 11 questions

  1. 2 Apr 2026, Shift 1 · Q11If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\sin\left(\frac{\pi}{18}\right)\sin\left(\frac{5\pi}{18}\right)\sin\left(\frac{7\pi}{18}\right)=K, then the value of…MediumSingle correct
  2. 2 Apr 2026, Shift 1 · Q12Let S={x∈[−π,π]:sin⁡x(sin⁡x+cos⁡x)=a,a∈Z}S=\{x \in [-\pi, \pi] : \sin x(\sin x+\cos x)=a, a \in \mathbb{Z}\}. Then n(S)n(S) is equal to :HardSingle correct
  3. 2 Apr 2026, Shift 2 · Q13Let P={θ∈[0,4π]:tan⁡2θ≠1}P = \{\theta \in [0, 4\pi]: \tan^2\theta \ne 1\} and…MediumSingle correct
  4. 2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram PQRSPQRS are given by PQ⃗=j^+k^\vec{PQ} = \hat{j} + \hat{k} and PS⃗=i^−j^\vec{PS} = \hat{i} - \hat{j}. If the side…MediumSingle correct
  5. 4 Apr 2026, Shift 1 · Q23If A=sin⁡3∘cos⁡9∘+sin⁡9∘cos⁡27∘+sin⁡27∘cos⁡81∘A=\frac{\sin 3^\circ}{\cos 9^\circ}+\frac{\sin 9^\circ}{\cos 27^\circ}+\frac{\sin 27^\circ}{\cos 81^\circ} and…MediumNumerical value
  6. 4 Apr 2026, Shift 1 · Q24Let a⃗k=(tan⁡θk)i^+j^\vec{a}_k=(\tan\theta_k)\hat{i}+\hat{j} and b⃗k=i^−(cot⁡θk)j^\vec{b}_k=\hat{i}-(\cot\theta_k)\hat{j}, where θk=2k−1π2n+1\theta_k=\frac{2^{k-1}\pi}{2^n+1},…HardNumerical value
  7. 5 Apr 2026, Shift 1 · Q6Let tan⁡A\tan A, tan⁡B\tan B, where A,B∈(−π2,π2)A, B \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right), be the roots of the quadratic equation…MediumSingle correct
  8. 5 Apr 2026, Shift 1 · Q12The sum of all the integral values of pp such that the equation 3sin⁡2x+12cos⁡x−3=p3\sin^2 x + 12\cos x - 3 = p, x∈Rx \in \mathbb{R}, has at least one…MediumSingle correct
  9. 5 Apr 2026, Shift 2 · Q23If S={θ∈[−π,π]:cos⁡θcos⁡5θ2=cos⁡7θcos⁡7θ2}S=\left\{\theta \in [-\pi, \pi] : \cos\theta\cos\frac{5\theta}{2}=\cos 7\theta\cos\frac{7\theta}{2}\right\}, then n(S) is equal to…HardNumerical value
  10. 6 Apr 2026, Shift 1 · Q14Let S={θ∈(−2π,2π):cos⁡θ+1=3sin⁡θ}\mathrm{S}=\left\{\theta\in(-2\pi,2\pi):\cos\theta+1=\sqrt{3}\sin\theta\right\}. Then ∑θ∈Sθ\sum_{\theta\in \mathrm{S}}\theta is equal to:MediumSingle correct
  11. 8 Apr 2026, Shift 2 · Q21The sum of squares of all the real solutions of the equation log⁡(x+1)(2x2+5x+3)=4−log⁡(2x+3)(x2+2x+1)\log_{(x+1)}(2x^2 + 5x + 3) = 4 - \log_{(2x+3)}(x^2 + 2x + 1) is equal to…MediumNumerical value

2025 6 questions

  1. 2 Apr 2025, Shift 1 · Q3If θ∈[−2π,2π]\theta\in[-2\pi, 2\pi], then the number of solutions of 22cos⁡2θ+(2−6)cos⁡θ−3=02\sqrt{2}\cos^2\theta+(2-\sqrt{6})\cos\theta-\sqrt{3}=0, is equal to :MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q13If θ∈[−7π6,4π3]\theta \in \left[-\frac{7\pi}{6}, \frac{4\pi}{3}\right], then the number of solutions of…MediumSingle correct
  3. 3 Apr 2025, Shift 1 · Q10The number of solutions of the equation 2x+3tan⁡x=π2x + 3\tan x = \pi, x∈[−2π,2π]−{±π2,±3π2}x \in [-2\pi, 2\pi] - \left\{\pm\frac{\pi}{2}, \pm\frac{3\pi}{2}\right\} is:MediumSingle correct
  4. 3 Apr 2025, Shift 2 · Q13The number of solutions of the equation…HardSingle correct
  5. 7 Apr 2025, Shift 1 · Q1If for θ∈[−π3,0]\theta \in \left[-\frac{\pi}{3}, 0\right], the points…MediumSingle correct
  6. 7 Apr 2025, Shift 2 · Q14The number of solutions of the equation cos⁡2θcos⁡θ2+cos⁡5θ2=2cos⁡35θ2\cos 2\theta\cos\frac{\theta}{2}+\cos\frac{5\theta}{2}=2\cos^3\frac{5\theta}{2} in…HardSingle correct

2024 7 questions

  1. 6 Apr 2024, Shift 2 · Q30In a triangle ABCABC, BC=7BC=7, AC=8AC=8, AB=α∈NAB=\alpha\in\mathbb{N} and cos⁡A=23\cos A=\frac{2}{3}. If 49cos⁡(3C)+42=mn49\cos(3C)+42=\frac{m}{n}, where…MediumNumerical value
  2. 8 Apr 2024, Shift 1 · Q20If sin⁡x=−35\sin x=-\frac{3}{5}, where π<x<3π2\pi<x<\frac{3\pi}{2}, then 80(tan⁡2x−cos⁡x)80(\tan^2x-\cos x) is equal toEasySingle correct
  3. 8 Apr 2024, Shift 1 · Q21If the range of f(θ)=sin⁡4θ+3cos⁡2θsin⁡4θ+cos⁡2θf(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}, θ∈R\theta\in\mathbb{R} is [α,β][\alpha,\beta], then…MediumNumerical value
  4. 9 Apr 2024, Shift 1 · Q20Let ∣cos⁡θcos⁡(60∘−θ)cos⁡(60∘+θ)∣≤18\left|\cos\theta\cos(60^\circ-\theta)\cos(60^\circ+\theta)\right|\le\frac{1}{8}, θ∈[0,2π]\theta\in[0,2\pi]. Then, the sum of all…MediumSingle correct
  5. 29 Jan 2024, Shift 1 · Q20If α,−π2<α<π2\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2} is the solution of 4cos⁡θ+5sin⁡θ=14\cos\theta+5\sin\theta=1, then the value of tan⁡α\tan\alpha isMediumSingle correct
  6. 30 Jan 2024, Shift 2 · Q11For α,β∈(0,π/2)\alpha, \beta \in (0, \pi/2), let 3sin⁡(α+β)=2sin⁡(α−β)3\sin(\alpha + \beta) = 2\sin(\alpha - \beta) and a real number kk be such that…MediumSingle correct
  7. 31 Jan 2024, Shift 2 · Q2The number of solutions, of the equation esin⁡x−2e−sin⁡x=2e^{\sin x}-2e^{-\sin x}=2, is :MediumSingle correct

2023 3 questions

  1. 6 Apr 2023, Shift 1 · Q19From the top A of a vertical wall AB of height 30 m, the angles of depression of the top P and bottom Q of a vertical tower PQ are…MediumSingle correct
  2. 8 Apr 2023, Shift 2 · Q19The value of 36(4cos⁡29∘−1)(4cos⁡227∘−1)(4cos⁡281∘−1)(4cos⁡2243∘−1)36(4\cos^2 9^\circ - 1)(4\cos^2 27^\circ - 1)(4\cos^2 81^\circ - 1)(4\cos^2 243^\circ - 1) isHardSingle correct
  3. 11 Apr 2023, Shift 1 · Q16The number of elements in the set S={θ∈[0,2π]:3cos⁡4θ−5cos⁡2θ−2sin⁡6θ+2=0}S = \{\theta \in [0, 2\pi] : 3\cos^4\theta - 5\cos^2\theta - 2\sin^6\theta + 2 = 0\} isMediumSingle correct

2022 5 questions

  1. 25 Jul 2022, Shift 1 · Q18The number of solutions of ∣cos⁡x∣=sin⁡x|\cos x|=\sin x, such that −4π≤x≤4π-4\pi\le x\le4\pi is :EasySingle correct
  2. 25 Jul 2022, Shift 1 · Q19A tower PQPQ stands on a horizontal ground with base QQ on the ground. The point RR divides the tower in two parts such that QR=15QR=15 m.…MediumSingle correct
  3. 24 Jun 2022, Shift 1 · Q19Let S={θ∈[−π,π]−{±π2}:sin⁡θtan⁡θ+tan⁡θ=sin⁡2θ}S=\left\{\theta\in[-\pi, \pi]-\left\{\pm\frac{\pi}{2}\right\}: \sin\theta\tan\theta+\tan\theta=\sin 2\theta\right\}. If…MediumSingle correct
  4. 29 Jun 2022, Shift 1 · Q24The number of elements in the set S={θ∈[−4π,4π]:3cos⁡22θ+6cos⁡2θ−10cos⁡2θ+5=0}S = \{\theta \in [-4\pi, 4\pi] : 3\cos^2 2\theta + 6\cos 2\theta - 10\cos^2\theta + 5 = 0\} is…MediumNumerical value
  5. 29 Jun 2022, Shift 1 · Q25The number of solutions of the equation 2θ−cos⁡2θ+2=02\theta - \cos^2\theta + \sqrt{2} = 0 in R\mathbf{R} is equal to ____________.MediumNumerical value

2021 6 questions

  1. 3 Aug 2021, Shift 2 · Q79The maximum value of (cos⁡θ1)⋅(cos⁡θ2)⋅(cos⁡θ3)⋅…⋅(cos⁡θ10)(\cos\theta_1)\cdot(\cos\theta_2)\cdot(\cos\theta_3)\cdot\ldots\cdot(\cos\theta_{10}) under the restrictions…HardSingle correct
  2. 3 Aug 2021, Shift 2 · Q89A vertical pole of height 10310\sqrt{3} meters is observed from three points, A, B and C in the same horizontal line passing through the…MediumNumerical value
  3. 25 Jul 2021, Shift 1 · Q73A spherical gas balloon of radius 16 meter subtends an angle 60∘60^\circ at the eye of the observer A while the angle of elevation of its…MediumSingle correct
  4. 25 Jul 2021, Shift 1 · Q80The sum of all values of xx in [0,2π][0,2\pi], for which sin⁡x+sin⁡2x+sin⁡3x+sin⁡4x=0\sin x+\sin2x+\sin3x+\sin4x=0, is equal to :MediumSingle correct
  5. 16 Mar 2021, Shift 2 · Q82In △\triangleABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of △\triangleABC is 30 cm2\mathrm{cm^2}…MediumNumerical value
  6. 18 Mar 2021, Shift 1 · Q90The number of solutions of the equation ∣cot⁡x∣=cot⁡x+1sin⁡x|\cot x|=\cot x+\dfrac{1}{\sin x} in the interval [0,2π][0,2\pi] is __________.MediumNumerical value

2020 1 questions

  1. 6 Sep 2020, Shift 2 · Q69The angle of elevation of the summit of a mountain from a point on the ground is 45∘45^\circ. After climbing up one km towards the summit…MediumSingle correct

2017 2 questions

  1. 2 Apr 2017 (offline) · Q88If 5(tan⁡2x−cos⁡2x)=2cos⁡2x+95(\tan^2x-\cos^2x)=2\cos2x+9, then the value of cos⁡4x\cos4x is :MediumSingle correct
  2. 2 Apr 2017 (offline) · Q89Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that…MediumSingle correct

Pattern: Asked most years.