Question

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

Explanation:

Step1: Recall sine definition

For an angle $\theta$ in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $60^\circ$

In the triangle, opposite side to $60^\circ$ is $8\sqrt{3}$, hypotenuse is $16$.

Step3: Calculate $\sin(60^\circ)$

$\sin(60^\circ) = \frac{8\sqrt{3}}{16} = \frac{\sqrt{3}}{2}$

Step4: Define input/output

The sine function takes an angle as input, outputs the ratio. So input is $60^\circ$, output is $\frac{\sqrt{3}}{2}$.

Answer:

B. input: $60^\circ$; output: $\frac{\sqrt{3}}{2}$