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 XI Mathematics

Chapter 3: Trigonometric Functions

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Key Formulas & Equations

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Radian Conversion Formula

\text{Radian} = \text{Degree} \times \frac{\pi}{180}

Converts angle from degree measures to radian metrics.

Pythagorean Identity

\sin^2 x + \cos^2 x = 1

Relates squared values of sine and cosine functions.

Related Formulas from Adjacent Chapters

Cartesian Product Cardinality

n(A \times B) = n(A) \times n(B)

[From Relations and Functions] Number of ordered pairs in Cartesian product.

Complex Number Polar Form

z = r(\cos\theta + i\sin\theta)

[From Complex Numbers and Quadratic Equations] Polar representation using modulus r and argument θ.

Modulus of Complex Number

|z| = \sqrt{x^2 + y^2}

[From Complex Numbers and Quadratic Equations] Magnitude of complex number x + iy.