NCERT Mathematics, Class 10, textbook pages 113–132

How to help your child with Class 10 Maths Chapter 8, Introduction to Trigonometry, at home

Trigonometric ratios and identities, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

θadjacentoppositehypotenusesin θ = opp/hyp

NCERT Class 10 Maths Chapter 8 Introduction to Trigonometry: what it teaches

In a right triangle, ratios of sides depend only on the angle. Your teen learns sin, cos, tan and their reciprocals, the values for 0°, 30°, 45°, 60°, 90°, and the identity sin²θ + cos²θ = 1.

Why it matters later. Trigonometry is used in Chapter 9, physics, engineering and Class 11 trigonometric functions.

See it: this chapter in pictures

θ: 0° 30° 45° 60° 90°sin: 0 ½ √2/2 √3/2 1cos: reverse order
A pattern makes values easy to remember.
tan A = 4/3hypotenuse = 5sin A = 4/5, cos A = 3/5
Draw the triangle.
opp² + adj² = hyp²÷ hyp²sin²θ + cos²θ = 1
Identities come from Pythagoras.

You need

  • a protractor and ruler
  • a calculator

Tonight’s 45 minutes

  1. Draw right triangles with a 30° angle of different sizes. Measure opposite ÷ hypotenuse: always 0.5.
  2. Make a table of sin, cos, tan for 0°, 30°, 45°, 60°, 90°.
  3. Given tan A = 4/3, find sin A and cos A (4/5, 3/5).
  4. Prove sin²θ + cos²θ = 1 using Pythagoras.

Words to use

  • sine
  • cosine
  • tangent
  • hypotenuse
  • opposite
  • adjacent
  • identity

Watch for

  • Mixing opposite and adjacent. Mark the angle first, then label sides from it.
  • Memorising values without pattern. Use √0/2, √1/2, √2/2, √3/2, √4/2 for sin 0° to 90°.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

Youtan A = 4/3. sin A?

Your childOpposite 4, adjacent 3, hypotenuse 5: 4/5.

A game for this week: Ratio memory

  1. Make cards for angles and ratios.
  2. Match sin 60° with √3/2 etc.
  3. Fastest correct matches win.
  4. Add reciprocal ratios later.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Ramps and slopes.
  • Roof pitches.
  • Navigation.
  • Physics of forces.

Quick check

Ask these at the end of the week. Tap to see the answer.

sin 30°?

½.

tan 45°?

1.

If tan A = 4/3, sin A?

4/5.

Ready for the next chapter when your child…

  • Defines the six ratios.
  • Recalls standard values.
  • Uses basic identities.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

How to remember sin values?

√0/2, √1/2, √2/2, √3/2, √4/2 for 0°, 30°, 45°, 60°, 90°.

Why do ratios depend only on angle?

All right triangles with that angle are similar.

What is sin²θ + cos²θ?

Always 1.