Trigonometric Identities — Part 1: The three Pythagorean identities: visual lesson, ICSE Class 10 Mathematics

Lesson

Trigonometric Identities, Part 1

An identity is true for every angle, not just one. Three of them follow from Pythagoras.

In this lesson you will

The three Pythagorean identities, and what to divide by.
Identity	Also written as	Divide $\sin^2\theta + \cos^2\theta = 1$ by
$\sin^2\theta + \cos^2\theta = 1$	$\sin^2\theta = 1 - \cos^2\theta$	nothing: it is the first form
$1 + \tan^2\theta = \sec^2\theta$	$\sec^2\theta - \tan^2\theta = 1$	$\cos^2\theta$
$1 + \cot^2\theta = \operatorname{cosec}^2\theta$	$\operatorname{cosec}^2\theta - \cot^2\theta = 1$	$\sin^2\theta$

Concept

One theorem, three identities.

Concept

In a right-angled triangle, for an acute angle $\theta$ :

For $\theta$ at $C$: opposite $6$, adjacent $8$, hypotenuse $10$, so $\sin\theta = \dfrac{3}{5}$, $\cos\theta = \dfrac{4}{5}$.