Simplify sin(0.0)

$\sin (0)$

Step 1

Rewrite $0$ as an angle where the values of the six trigonometric functions are known divided by $2$ .

$\sin (\frac{0}{2})$

Step 2

Apply the sine half-angle identity.

$\pm \sqrt{\frac{1 - \cos (0)}{2}}$

Step 3

Change the $\pm$ to $+$ because sine is positive in the first quadrant.

$\sqrt{\frac{1 - \cos (0)}{2}}$

Step 4

Simplify $\sqrt{\frac{1 - \cos (0)}{2}}$ .

The exact value of $\cos (0)$ is $1$ .

$\sqrt{\frac{1 - 1 \cdot 1}{2}}$

Multiply $- 1$ by $1$ .

$\sqrt{\frac{1 - 1}{2}}$

Subtract $1$ from $1$ .

$\sqrt{\frac{0}{2}}$

Divide $0$ by $2$ .

$\sqrt{0}$

Rewrite $0$ as $0^{2}$ .

$\sqrt{0^{2}}$

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

$0$