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What is [tex]\sin 62^{\circ}[/tex]?

A. [tex]\frac{8}{17}[/tex]

B. [tex]\frac{15}{17}[/tex]

C. [tex]\frac{15}{8}[/tex]

D. [tex]\frac{8}{15}[/tex]


Sagot :

To find [tex]\(\sin 62^{\circ}\)[/tex], we need to compare the value of [tex]\(\sin 62^{\circ}\)[/tex] to the given choices and determine which one is closest.

First, consider the sine values of the choices provided. We convert the fractions to their decimal form for easy comparison:

1. [tex]\(\frac{8}{17} \approx 0.4706\)[/tex]
2. [tex]\(\frac{15}{17} \approx 0.8824\)[/tex]
3. [tex]\(\frac{15}{8} \approx 1.8750\)[/tex]
4. [tex]\(\frac{8}{15} \approx 0.5333\)[/tex]

Now, we know from trigonometric tables or a calculator that the value of [tex]\(\sin 62^{\circ}\)[/tex] is approximately [tex]\(0.8824\)[/tex].

Comparing the value [tex]\(0.8824\)[/tex] to our given choices:
- [tex]\(\frac{8}{17} \approx 0.4706\)[/tex]
- [tex]\(\frac{15}{17} \approx 0.8824\)[/tex]
- [tex]\(\frac{15}{8} \approx 1.8750\)[/tex]
- [tex]\(\frac{8}{15} \approx 0.5333\)[/tex]

It's clear that the fraction [tex]\(\frac{15}{17}\)[/tex] is the closest to the actual value of [tex]\(\sin 62^{\circ}\)[/tex].

Therefore, the correct answer is [tex]\( \boxed{\frac{15}{17}} \)[/tex], which corresponds to option B.