# $\sin{(90^°)}$ value

The sin value when angle of a right triangle equals to $90^°$ is called sine of angle $90$ degrees. In mathematics, it is written as $\sin{(90^°)}$ according to sexagesimal system.

$\sin{(90^°)} \,=\, 1$

The value of sin of $90$ degrees is $1$ exactly and it is often called as trigonometric function (or ratio) for standard angle generally.

## Alternative form

The $\sin{(90^°)}$ is expressed alternatively as $\sin{\Big(\dfrac{\pi}{2}\Big)}$ in circular system and also expressed mathematically as $\sin{(100^g)}$ in centesimal system.

$(1) \,\,\,$ $\sin{\Big(\dfrac{\pi}{2}\Big)} \,=\, 1$

$(2) \,\,\,$ $\sin{(100^g)} \,=\, 1$

### Proof

You just learnt that the exact value of sin of $90$ degrees is $1$ and it is your turn to learn how the value of $\sin{\Big(\dfrac{\pi}{2}\Big)}$ is equal to one mathematically from a geometric proof.

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