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Cheat sheet · JEE Preparation 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.

JEE · Mathematics

Cheat sheet

Class 11 · 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

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