Question

what are the input and output values for determining the sine of 60°?
o input: 60°; output: $\frac{sqrt{3}}{2}$
o input: $\frac{sqrt{3}}{2}$; output: 60°
o input: 60°; output: $\frac{2}{sqrt{3}}$
o input: $\frac{2}{sqrt{3}}$; output: 60°

Explanation:

Step1: Recall sine - function definition

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for 60° angle

In right - triangle $ABC$, for the $60^{\circ}$ angle at $B$, the opposite side to the $60^{\circ}$ angle is $AC = 8\sqrt{3}$ and the hypotenuse is $AB = 16$.

Step3: Calculate $\sin60^{\circ}$

$\sin60^{\circ}=\frac{8\sqrt{3}}{16}=\frac{\sqrt{3}}{2}$. The input is the angle $60^{\circ}$ and the output is the ratio $\frac{\sqrt{3}}{2}$.

Answer:

Input: $60^{\circ}$; output: $\frac{\sqrt{3}}{2}$