To determine the correct input and output values for finding the sine of [tex]$60^{\circ}$[/tex], let's go through the possible choices:
1. Option A: input: [tex]\(\frac{2}{\sqrt{3}}\)[/tex]; output: [tex]\(60^{\circ}\)[/tex]
- This is incorrect because [tex]\(\frac{2}{\sqrt{3}}\)[/tex] is not standardly related to the sine of [tex]\(60^{\circ}\)[/tex].
2. Option B: input: [tex]\(60^{\circ}\)[/tex]; output: [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
- This is the correct choice. The sine of [tex]\(60^{\circ}\)[/tex] is known to be [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
3. Option C: input: [tex]\(60^{\circ}\)[/tex]; output: [tex]\(\frac{2}{\sqrt{3}}\)[/tex]
- This is incorrect because, as mentioned, the sine of [tex]\(60^{\circ}\)[/tex] is not [tex]\(\frac{2}{\sqrt{3}}\)[/tex].
4. Option D: input: [tex]\(\frac{\sqrt{3}}{2}\)[/tex]; output: [tex]\(60^{\circ}\)[/tex]
- This is incorrect in the context of evaluating the sine function. It would be correct if the question were about finding the angle whose sine is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
Given these points, the correct input and output values for determining the sine of [tex]\(60^{\circ}\)[/tex] are:
input: [tex]\(60^{\circ}\)[/tex]; output: [tex]\(\frac{\sqrt{3}}{2}\)[/tex]
