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.

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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.

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Key Formulas & Equations

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Sine Inverse range

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

Principal value branch for arcsin.

Related Formulas from Adjacent Chapters

Composition of Functions

(g \circ f)(x) = g(f(x))

[From Relations and Functions] Evaluates function g on the output of function f.

Matrix Inverse Formula

A^{-1} = \frac{1}{|A|} \text{adj}(A)

[From Matrices and Determinants] Inverse of square matrix A using determinant and adjoint.

Determinant Expansion 2x2

\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

[From Matrices and Determinants] Evaluation of 2x2 determinant.