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Cheat sheet · Class 10 · CBSE Mathematics

Introduction to Trigonometry cheat sheet

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

CBSE Class 10 · Mathematics

Cheat sheet

Chapter 8Introduction to Trigonometry

Some People Have Curly Brown Hair Through Proper Brushing.

1. Trigonometric Ratios

In right △ABC\triangle ABC (right angle at B), for angle AA:

sin⁡A=PH\sin A = \dfrac{P}{H}cos⁡A=BH\cos A = \dfrac{B}{H}tan⁡A=PB\tan A = \dfrac{P}{B}
cosec⁡A=1sin⁡A\operatorname{cosec} A = \dfrac{1}{\sin A}sec⁡A=1cos⁡A\sec A = \dfrac{1}{\cos A}cot⁡A=1tan⁡A\cot A = \dfrac{1}{\tan A}
tan⁡A=sin⁡Acos⁡A\tan A = \dfrac{\sin A}{\cos A}cot⁡A=cos⁡Asin⁡A\cot A = \dfrac{\cos A}{\sin A}

P = perpendicular (opposite), B = base (adjacent), H = hypotenuse. Ratios depend only on the angle, not the triangle size.

2. Identities

sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1
1+tan⁡2A=sec⁡2A1 + \tan^2 A = \sec^2 A(0∘≤A<90∘)(0^\circ \le A < 90^\circ)
1+cot⁡2A=cosec⁡2A1 + \cot^2 A = \operatorname{cosec}^2 A(0∘<A≤90∘)(0^\circ < A \le 90^\circ)

Proof tips

  • Convert everything to sin and cos
  • Start from the more complicated side
  • Use a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b) and rationalise

3. Standard Values

Ratio0°30°45°60°90°
sin012\dfrac{1}{2}12\dfrac{1}{\sqrt{2}}32\dfrac{\sqrt{3}}{2}1
cos132\dfrac{\sqrt{3}}{2}12\dfrac{1}{\sqrt{2}}12\dfrac{1}{2}0
tan013\dfrac{1}{\sqrt{3}}13\sqrt{3}not defined
cosecnot defined22\sqrt{2}23\dfrac{2}{\sqrt{3}}1
sec123\dfrac{2}{\sqrt{3}}2\sqrt{2}2not defined
cotnot defined3\sqrt{3}113\dfrac{1}{\sqrt{3}}0

Trick: sin values = 04,14,24,34,44\sqrt{\frac{0}{4}}, \sqrt{\frac{1}{4}}, \sqrt{\frac{2}{4}}, \sqrt{\frac{3}{4}}, \sqrt{\frac{4}{4}}; cos is the reverse.

4. Remember

  • 0≤sin⁡A,cos⁡A≤10 \le \sin A, \cos A \le 1 for acute A
  • sin increases, cos decreases from 0° to 90°
  • sec⁡A,cosec⁡A≥1\sec A, \operatorname{cosec} A \ge 1
  • Given one ratio, draw a triangle and use Pythagoras to find the rest

5. Key Points to Remember

  • sin A = P/H, cos A = B/H, tan A = P/B.
  • sin²A + cos²A = 1.
  • tan 45° = 1; tan 90° is not defined.
  • sin 30° = cos 60° = ½.
  • Reciprocal pairs: sin–cosec, cos–sec, tan–cot.
  • Write a value table from memory before solving.

Remember: SOH-CAH-TOA | sin² + cos² = 1 | 1 + tan² = sec²

Introduction to Trigonometry: questions and notes

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