Answer :
To determine the sine of [tex]\(60^\circ\)[/tex], we need to identify the correct input and output values associated with this trigonometric function.
### Step-by-Step Solution:
1. Understanding the Question:
- We are asked to determine the input and output values for the sine function where the angle is [tex]\(60^\circ\)[/tex].
- The input value is the angle given in degrees.
- The output value is the sine of that angle.
2. Identifying the Input:
- The input value in this problem is the angle, which is given as [tex]\(60^\circ\)[/tex]. Therefore, the input for the function is [tex]\(60^\circ\)[/tex].
3. Identifying the Output:
- The output value is the sine of the input angle.
- The sine of [tex]\(60^\circ\)[/tex] is a well-known trigonometric value.
- We know that the sine of [tex]\(60^\circ\)[/tex] is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
4. Matching Input and Output:
- Given an angle of [tex]\(60^\circ\)[/tex] (input), the sine value (output) is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
### Conclusion:
Given the input angle [tex]\(60^\circ\)[/tex], the sine function returns an output of [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
Therefore, 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]
So, the correct choice is:
[tex]\[ \text{input: } 60^{\circ}; \text{ output: } \frac{\sqrt{3}}{2} \][/tex]
### Step-by-Step Solution:
1. Understanding the Question:
- We are asked to determine the input and output values for the sine function where the angle is [tex]\(60^\circ\)[/tex].
- The input value is the angle given in degrees.
- The output value is the sine of that angle.
2. Identifying the Input:
- The input value in this problem is the angle, which is given as [tex]\(60^\circ\)[/tex]. Therefore, the input for the function is [tex]\(60^\circ\)[/tex].
3. Identifying the Output:
- The output value is the sine of the input angle.
- The sine of [tex]\(60^\circ\)[/tex] is a well-known trigonometric value.
- We know that the sine of [tex]\(60^\circ\)[/tex] is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
4. Matching Input and Output:
- Given an angle of [tex]\(60^\circ\)[/tex] (input), the sine value (output) is [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
### Conclusion:
Given the input angle [tex]\(60^\circ\)[/tex], the sine function returns an output of [tex]\(\frac{\sqrt{3}}{2}\)[/tex].
Therefore, 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]
So, the correct choice is:
[tex]\[ \text{input: } 60^{\circ}; \text{ output: } \frac{\sqrt{3}}{2} \][/tex]
