Trigonometry Examples

$\sin (x) = \sqrt{1 - \cos^{2} (x)}$

Step 1

Start on the right side.

$\sqrt{1 - \cos^{2} (x)}$

Step 2

Simplify the expression.

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Step 2.1

Apply pythagorean identity.

$\sqrt{\sin^{2} (x)}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\sin (x)$

Step 3

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sin (x) = \sqrt{1 - \cos^{2} (x)}$ is an identity