What is a radian and why is it used?

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. It is the natural unit for angles in calculus and advanced physics because it simplifies equation relations (e.g. d/dx[sinx] = cosx is only true when x is in radians).

What is the ASTC rule?

The "All Science Teachers Crazy" (or Cast) rule indicates where trig functions are positive: All are positive in Quad I, Sin in Quad II, Tan in Quad III, and Cos in Quad IV.

Back to Class XII Mathematics

Class XII Mathematics

Chapter 2: Inverse Trigonometric Functions

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

Select Syllabus Tab:

Syllabus Sections

Print-Ready Math Worksheet

Generate and print a beautiful chapter worksheet complete with key equations, problems, and dedicated writing spaces.

Worksheet Details:

• Title: Class XII Math: Inverse Trigonometric Functions Printable Sheet
• Format: Print Optimized CSS stylesheet
• Sections: Formulas checklist, 5 assessment questions, worked keys

NexPro Education Worksheet

Class XII Mathematics: Inverse Trigonometric Functions

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

Sine Inverse range

\sin^{-1} x = \theta \Rightarrow \theta \in [-\frac{\pi}{2}, \frac{\pi}{2}]

Section II: Answer the Questions

1. Find the value of sin-1[cos( 33π 5 )]

Solve and write the step-by-step solution in the workspace below.

2. Assertion (A): Maximum value of (cos-1 x)2 is π2. Reason (R): Range of the principal value branch of cos-1 x is ,2 2 π π-[ ] [ ][ ]

[ ] A. Option A[ ] B. Option B[ ] C. Option C[ ] D. Option D

3. The differential coefficient of sec(tan-1 x ) w.r.t. x is

[ ] A. x √1/x2[ ] B. x 1/x2[ ] C. x √1 +x2[ ] D. 1 √1/x2

4. Assertion (A) : The value of expression 1 1 1 2 1sec tan 1 sin 23 - - -( ) ( )+ + ( )( ) ( )( ) is 4 π Reason (R) : Principal value branch of 1 sin x - is ,2 2 π π[ ]-[ ][ ] and that of 1 sec x - is [0, ] { / 2}π π-

[ ] A. Option A[ ] B. Option B[ ] C. Option C[ ] D. Option D

5. The domain, for which tan-1x > cot-1x holds true, is:

[ ] A. x = 1[ ] B. x > 1[ ] C. x < 1[ ] D. Not defined

Recommended Worksheets from Other Chapters

Worksheet

Download Worksheet: Inverse Trigonometric Functions

Chapter: Inverse Trigonometric Functions

Open Sheet

Worksheet

Adjacent Worksheet: Relations and Functions

Chapter: Relations and Functions

Open Sheet

Worksheet

Adjacent Worksheet: Matrices and Determinants

Chapter: Matrices and Determinants

Open Sheet