Inverse Trigonometric Functions — Class 12 CBSE Mathematics revision notes
A 3-page visual revision sheet for Inverse Trigonometric Functions, written for Class 12 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Inverse Trigonometric Functions in one look
restrict the domain first, then the arrow can run backward
sin⁻¹, cos⁻¹, tan⁻¹: principal branches
- sin^-1x
[-1,1] to [-π/2,π/2] - cos^-1x
[-1,1] to [0,π] - tan^-1x
R to (-π/2,π/2)
Reading a principal branch
- each graph is just one strand chosen from the full periodic curve, cut so it's monotonic
- sin^-1x and tan^-1x are both increasing on their branch
- cos^-1x is decreasing, running from π down to 0 as x goes from -1 to 1
sin⁻¹x vs cos⁻¹x, same input
- odd function: sin^-1(-x) = -sin^-1x
- passes through the origin: sin^-10 = 0
- neither odd nor even: cos^-1(-x) = π - cos^-1x
- cos^-10 = π/2, not 0
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Inverse Trigonometric Functions sheet covers
- Basic Concepts and Range
- Why the domain must shrink first
- sin⁻¹, cos⁻¹, tan⁻¹: principal branches
- sin^-1x
- cos^-1x
- tan^-1x
- Reading a principal branch
- sin⁻¹x vs cos⁻¹x, same input
- sin⁻¹x
- cos⁻¹x
- cot⁻¹, sec⁻¹, cosec⁻¹: principal branches
- cot^-1x
- sec^-1x
- cosec^-1x
- Properties of Inverse Trigonometric Functions
- Reciprocal relations
- sine and cosecant
- cosine and secant
- tangent and cotangent, x>0
- tan⁻¹x + tan⁻¹y
- sum, safe zone
- difference, xy>-1
- tan⁻¹x + tan⁻¹y: when the correction kicks in
- Double: 2tan⁻¹x
- double-angle style form, |x|<1
- Three pairs that sum to π/2
- sin⁻¹x + cos⁻¹x
- tan⁻¹x + cot⁻¹x
- sec⁻¹x + cosec⁻¹x
- Negative input: flip sign, or flip through π
- Symbols
- Worked: using the double-angle formula
- Reading identities together
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Inverse Trigonometric Functions the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.