KTUYSBeta
Log inSign up

Cheat sheet · Class 11 · CBSE · Commerce Mathematics

Trigonometric Functions cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

CBSE Class 11 · Mathematics

Cheat sheet

Chapter 3Trigonometric Functions

ASTC — All, Sin, Tan, Cos are positive in quadrants I, II, III, IV.

1. Angles

π rad=180∘\pi\ \text{rad} = 180^\circl=rθl = r\theta

1 rad≈57∘16′1\ \text{rad} \approx 57^\circ 16'.

2. Allied Angles

  • sin⁡(−x)=−sin⁡x\sin(-x) = -\sin x, cos⁡(−x)=cos⁡x\cos(-x) = \cos x.
  • sin⁡(π−x)=sin⁡x\sin(\pi - x) = \sin x, cos⁡(π−x)=−cos⁡x\cos(\pi - x) = -\cos x.
  • sin⁡(π2−x)=cos⁡x\sin(\tfrac\pi2 - x) = \cos x; period of sin, cos is 2π2\pi, of tan is π\pi.

3. Sum & Multiple Angle Formulas

sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B\sin(A\pm B) = \sin A\cos B\pm\cos A\sin B
cos⁡(A±B)=cos⁡Acos⁡B∓sin⁡Asin⁡B\cos(A\pm B) = \cos A\cos B\mp\sin A\sin B
tan⁡(A±B)=tan⁡A±tan⁡B1∓tan⁡Atan⁡B\tan(A\pm B) = \dfrac{\tan A\pm\tan B}{1\mp\tan A\tan B}
sin⁡2x=2sin⁡xcos⁡x\sin2x = 2\sin x\cos xcos⁡2x=1−2sin⁡2x=2cos⁡2x−1\cos2x = 1 - 2\sin^2x = 2\cos^2x - 1
sin⁡3x=3sin⁡x−4sin⁡3x\sin3x = 3\sin x - 4\sin^3xcos⁡3x=4cos⁡3x−3cos⁡x\cos3x = 4\cos^3x - 3\cos x

4. Sum to Product

sin⁡C+sin⁡D=2sin⁡C+D2cos⁡C−D2\sin C + \sin D = 2\sin\tfrac{C + D}{2}\cos\tfrac{C - D}{2}
cos⁡C+cos⁡D=2cos⁡C+D2cos⁡C−D2\cos C + \cos D = 2\cos\tfrac{C + D}{2}\cos\tfrac{C - D}{2}
cos⁡C−cos⁡D=−2sin⁡C+D2sin⁡C−D2\cos C - \cos D = -2\sin\tfrac{C + D}{2}\sin\tfrac{C - D}{2}

5. Key Points

  • sin x = 0 ⇔ x = nπ.
  • cos x = 0 ⇔ x = (2n + 1)π/2.
  • |sin x|, |cos x| ≤ 1.
  • Memorise values at 0°, 30°, 45°, 60°, 90°.

Remember: Radian | ASTC | compound & multiple angles

Trigonometric Functions: questions and notes

More Class 11 · CBSE · Commerce Mathematics cheat sheets

Practise Trigonometric Functions

Sign up free to practise the full chapter. Questions you get wrong come back until you've mastered them.

Start practising free

Free to start · No credit card needed