What are the input and output values for determining the sine of [tex]\( 60^{\circ} \)[/tex]?

A. input: [tex]\( \frac{2}{\sqrt{3}} \)[/tex]; output: [tex]\( 60^{\circ} \)[/tex]
B. input: [tex]\( 60^{\circ} \)[/tex]; output: [tex]\( \frac{\sqrt{3}}{2} \)[/tex]
C. input: [tex]\( 60^{\circ} \)[/tex]; output: [tex]\( \frac{2}{\sqrt{3}} \)[/tex]
D. input: [tex]\( \frac{\sqrt{3}}{2} \)[/tex]; output: [tex]\( 60^{\circ} \)[/tex]



Answer :

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]