Chapter 8 · Class X Mathematics · NCERT Exercises

Introduction to Trigonometry — Exercises

Ratios · Identities · Standard Values — 27 Trig Problems Solved

📂 3 Exercises 📝 22 Questions 🎓 High

▶ Start Exercises 📖 Revise Notes

Exercise Index

Trig ratios from right triangle; evaluate given one ratio

11 Q Easy-Moderate

Standard values at 0°, 30°, 45°, 60°, 90°; evaluate expressions

Complementary angles: sin θ = cos(90°−θ) etc.

3 exercise files · 22 total questions

Chapter at a Glance

CBSE BoardsNTSEJEE Foundation

11 Concepts

20 Formulas

High Difficulty

8–10% Weightage

Before You Begin

Prerequisites

✓Right-angle triangles (Pythagoras)
✓Algebraic identities
✓Basic angle knowledge

Have Ready

🔧Standard values table (0°–90°)
🔧Unit right-triangle diagram
🔧Identity proof checklist

Exercise Topic Map

Exercise 8.1 From right △ with given ratio: draw and label triangle; compute hypotenuse via Pythagoras; find all six ratios

Exercise 8.2 Memorise table: sin30°=½, cos45°=1/√2, tan60°=√3 etc.; substitute and simplify

Exercise 8.3 sin A = cos(90°−A); tan A = cot(90°−A); convert to make angles equal

Key Formulae — Recall Before Solving

\(\sin^2\theta + \cos^2\theta = 1;\quad 1+\tan^2\theta = \sec^2\theta;\quad 1+\cot^2\theta = \csc^2\theta\)

\(\sin(90°-\theta)=\cos\theta;\quad \tan(90°-\theta)=\cot\theta\)

\(\sin 30°=\tfrac{1}{2},\ \cos 30°=\tfrac{\sqrt{3}}{2},\ \tan 30°=\tfrac{1}{\sqrt{3}}\)

\(\sin 45°=\cos 45°=\tfrac{1}{\sqrt{2}};\quad \sin 60°=\tfrac{\sqrt{3}}{2},\ \tan 60°=\sqrt{3}\)

NCERT Solving Method

Step 1 — Given ratio: sketch a right triangle; label opposite, adjacent, hypotenuse; find missing side via Pythagoras. Step 2 — Identity proofs: ALWAYS work on ONE side; convert everything to sin and cos if stuck. Step 3 — Standard values: memorise the table; for 0° and 90° recall sin0°=0, cos90°=0, tan90°=undefined. Step 4 — Complementary angles: if two angles sum to 90°, swap trig function (sin↔cos, tan↔cot, sec↔cosec).

Continue Your Preparation

📖NotesTheory & concepts 🧠MCQsTopic-wise practice ⚖️True–FalseConcept check ➡️Next ChapterApplications of Trigonometry

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