NCERT Mathematics, Class 12, textbook pages 18–33 (Part I)

How to help your child with Class 12 Maths Chapter 2, Inverse Trigonometric Functions, at home

Principal values and graphs, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

sin⁻¹ x ∈ [−π/2, π/2]cos⁻¹ x ∈ [0, π]tan⁻¹ x ∈ (−π/2, π/2)

NCERT Class 12 Maths Chapter 2 Inverse Trigonometric Functions: what it teaches

Your teen learns the inverse trig functions sin⁻¹, cos⁻¹, tan⁻¹ and others, their domains and principal value ranges, graphs and basic properties.

Why it matters later. Inverse trig functions appear in integration and differential equations.

See it: this chapter in pictures

sin⁻¹(½) = π/6cos⁻¹(−½) = 2π/3within principal ranges
Always check the range.
tan⁻¹(1) + cos⁻¹(0)= π/4 + π/2= 3π/4
Evaluate each, then add.
sin⁻¹ x ≠ 1/sin x1/sin x = cosec x⁻¹ means inverse
Inverse, not reciprocal.

You need

  • graph paper
  • a calculator

Tonight’s 60 minutes

  1. Why restrict sin x to [−π/2, π/2] to make an inverse?
  2. Find sin⁻¹(½) = π/6 and cos⁻¹(−½) = 2π/3.
  3. Sketch y = sin⁻¹ x by reflecting y = sin x in y = x.
  4. Evaluate tan⁻¹(1) + cos⁻¹(0).

Words to use

  • inverse function
  • principal value
  • domain
  • range
  • restriction

Watch for

  • Giving values outside the principal range. Memorise ranges: sin⁻¹ [−π/2, π/2], cos⁻¹ [0, π], tan⁻¹ (−π/2, π/2).
  • Reading sin⁻¹ x as 1/sin x. sin⁻¹ is the inverse, not the reciprocal.

What it sounds like at home

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

Youcos⁻¹(−½)?

Your childIn [0, π]: 2π/3.

A game for this week: Range race

  1. Call an inverse trig expression.
  2. Players give the principal value.
  3. Check ranges.
  4. Fastest correct wins.

A 5-day plan, 60 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

  • Angle from slope (tan⁻¹).
  • Navigation angles.
  • Engineering design.
  • Robotics joints.

Quick check

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

sin⁻¹(½)?

π/6.

cos⁻¹(−½)?

2π/3.

tan⁻¹(1) + cos⁻¹(0)?

3π/4.

Ready for the next chapter when your child…

  • States domains and principal ranges.
  • Evaluates principal values.
  • Sketches inverse trig graphs.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

Why do we need principal values?

Trig functions repeat, so we restrict domains to make inverses.

Is sin⁻¹ x the same as 1/sin x?

No; 1/sin x is cosec x.

Where are they used?

In integration and angle calculations.