Quick answer: Trigonometry (Chapters 8 and 9) is worth about 12 marks in Class 10 boards — a ratios/identities question and a heights-and-distances application. Both are formula-based.
The six ratios
In a right triangle with angle θ: sin θ = P/H, cos θ = B/H, tan θ = P/B, cosec = H/P, sec = H/B, cot = B/P. Trick: Some People Have Curly Brown Hair Through Proper Brushing.
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Table
| 0° | 30° | 45° | 60° | 90° | |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan | 0 | 1/√3 | 1 | √3 | not defined |
Complementary angles
- sin(90° − θ) = cos θ; tan(90° − θ) = cot θ; sec(90° − θ) = cosec θ
- Example: sin 18°/cos 72° = 1
Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
- Example proof: (1 + cot θ − cosec θ)(1 + tan θ + sec θ) = 2 — multiply out and use identities.
Heights and distances
Angle of elevation (looking up) and depression (looking down, equal to the elevation from the other point). Draw the figure, mark the right angle, use tan for height/base.
Example: From a point 30 m from the foot of a tower, the angle of elevation of the top is 60°. Height = 30 tan 60° = 30√3 ≈ 52 m.
Example: A kite’s string is 100 m at 30° → height = 100 sin 30° = 50 m.
Ratios from one ratio
If tan θ = 3/4: P = 3k, B = 4k, H = 5k → sin θ = 3/5, cos θ = 4/5.
Common mistakes
- Using the tan table value for 90°
- Mixing angle of elevation and depression in the figure
- Forgetting to rationalise (1/√3 = √3/3)
Related: Triangles Class 10.
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Frequently asked questions
Are these Trigonometry Class 10 Notes notes enough for the exam?
They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.
How should I revise Trigonometry Class 10 Notes?
Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.
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