Question

`sin` of what is equal to `sqrt3/2`?

Answer 1

`sin60` degrees or `pi/3` radians

Explanation:

In a 30-60-90 triangle, the sides are in the ratio `x:xsqrt3:2x` (smallest leg:longest leg:hypotenuse).

`sin` is opposite side over hypotenuse

The opposite side for the `90` degree angle is the hypotenuse, so `sin90` is `1`

The opposite side for the `30` degree angle is the smallest leg (`x`).

The opposite side for the `60` degree angle is the longest leg (`xsqrt3`). `(xsqrt3)/(2x)=sqrt3/2`

Answer 2

`rarrx=npi+(-1)^n*(pi/3)` where `n rarrZ`

Explanation:

Let `sinx=sqrt3/2`

`rarrsinx=sin(pi/3)`

`rarrx=npi+(-1)^n*(pi/3)` where `n rarrZ`