📐 Basic Trigonometry for Programming

Last Updated: Jan 2026

Trigonometry deals with the relationship between angles and sides of a triangle. In programming, it is used for:

🗣 Hinglish Tip: Trigonometry = angle se distance nikalna

Right-Angled Triangle Basics

A Pythagorean Identity is a relationship between the sides of a right triangle.

Pythagorean Identities

 $\sin^2\theta + \cos^2\theta = 1$

 $1 + \tan^2\theta = \sec^2\theta$

 $1 + \cot^2\theta = \cosec^2\theta$

Standard Angle Values

Angle	sin	cos	tan	cosec	sec	cot
$0^\circ$	0	1	0	$\infty$	1	$\infty$
$30^\circ$	1/2	$\sqrt3/2$	$1/\sqrt3$	2	$2/\sqrt3$	$\sqrt3$
45°	$1/\sqrt2$	$1/\sqrt2$	1	$\sqrt2$	$\sqrt2$	1
$60^\circ$	$\sqrt3/2$	1/2	$\sqrt3$	$2/\sqrt3$	2	$1/\sqrt3$
$90^\circ$	1	0	$\infty$	1	$\infty$	0

🗣 Hinglish Tip: Coding me mostly $30^\circ,\ 45^\circ,\ 60^\circ$ use hote hain

Conversion Formula

 $\text{radian} = \text{degree} \times \frac{\pi}{180}$

 $\text{degree} = \text{radian} \times \frac{180}{\pi}$

Example

 $90^\circ = \frac{\pi}{2}\text{ radians}$

Important ⚠️ : Most programming languages (Python, JS, C++) use radians, not degrees.

Distance Between Two Points

 $\text{distance} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

Angle Between Two Points

 $\theta = \tan^{-1}\left(\frac{y_2-y_1}{x_2-x_1}\right)$

Used in: