What is [tex]\sin 16^{\circ}[/tex]?

A. [tex]\frac{24}{7}[/tex]

B. [tex]\frac{24}{25}[/tex]

C. [tex]\frac{7}{25}[/tex]

D. [tex]\frac{7}{24}[/tex]



Answer :

To find the value of \(\sin 16^{\circ}\), we need to compare the given options with the actual sine value of 16 degrees.

### Step-by-Step Solution:

1. Convert Degrees to Radians:
The sine function in most contexts uses radians, so we first need to convert 16 degrees to radians.
[tex]\[ \text{Radians} = 16^\circ \times \frac{\pi}{180^\circ} \][/tex]
However, the key point here is to use the correct value corresponding to sine of 16 degrees.

2. Approximate the Value:
From trigonometric tables or a calculator, we find that:
[tex]\[ \sin 16^{\circ} \approx 0.2756 \][/tex]

3. Evaluate Each Option:
Next, we convert each fraction to a decimal to compare with 0.2756.

- Option A: \(\frac{24}{7} \approx 3.4286\)
- Option B: \(\frac{24}{25} = 0.96\)
- Option C: \(\frac{7}{25} = 0.28\)
- Option D: \(\frac{7}{24} \approx 0.2917\)

We see that amongst these values, \(\frac{7}{25}\) \(\approx 0.28\) is the closest to 0.2756.

4. Identify the Closest Match:
Since \(\frac{7}{25}\) is approximately 0.28, which is closest to the actual sine value of 16 degrees (0.2756), we conclude that the correct match is option C.

### Conclusion:
[tex]\[ \boxed{C} \][/tex]
Thus, the value of [tex]\(\sin 16^{\circ}\)[/tex] is best approximated by [tex]\(\frac{7}{25}\)[/tex].