## Pythagorus Theorem

For right-angled triangles, the Pythagorus Theorem lets us calculate a side length from any of the other two.

The Pythagorus Theor￼em is:

$a^2 + b^2 = c^2$

In the case of the 3, 4, 5 triangle (see previous section), then:

$3^2 + 4^2 = 5^2$
$9 + 16 = 25$

If we’re missing a side length, then we can use it to work backwards.

$x^2 + 4^2 = 5^2$
$x^2 + 16 = 25$
$x^2 = 9$
$x = 3$

If we look at a triangle whose hypotenuse is of length 1, the other two sides (going back to the SohCahToa) have a length of sinθ and cosθ. The Pythagorus Theorem gives us:

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

This is known as the Pythagorean Identity. It relates sine and cosine to each other and is an important tool for manipulating and simplifying trigonometric equations.

Back up to Trigonometry

### Proof

Back up to Trigonometry

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