To find [tex]\(\sin 62^\circ\)[/tex], follow these steps:
1. Convert the angle from degrees to radians:
The sine function in trigonometry is usually calculated in radians when using mathematical tools. The conversion from degrees to radians is given by:
[tex]\[
\text{{radians}} = \text{{degrees}} \times \left(\frac{\pi}{180}\right)
\][/tex]
For [tex]\(62^\circ\)[/tex]:
[tex]\[
\text{{radians}} = 62 \times \left(\frac{\pi}{180}\right) \approx 1.0821
\][/tex]
2. Calculate the sine of the angle in radians:
Now, use the sine function to find the sine of [tex]\(1.0821\)[/tex] radians. This can often be done using a scientific calculator or a mathematical software tool.
[tex]\[
\sin(1.0821) \approx 0.8829
\][/tex]
3. Compare the calculated value with the given options:
None of the provided options (A, B, C, D) match the value we obtained, which is approximately [tex]\(0.8829\)[/tex].
Therefore, it's necessary to conclude that none of the given options (A. [tex]\(\frac{8}{17}\)[/tex], B. [tex]\(\frac{15}{8}\)[/tex], C. [tex]\(\frac{8}{15}\)[/tex], D. [tex]\(\frac{15}{17}\)[/tex]) are correct for the value of [tex]\(\sin 62^\circ\)[/tex]. The correct value is approximately [tex]\(0.8829\)[/tex].
