To solve the equation [tex]\(\sin(x) = \frac{1}{7}\)[/tex] and find [tex]\(x\)[/tex] in degrees, we follow these steps:
1. Calculate the Inverse Sine: We start by finding [tex]\(x\)[/tex] in radians using the inverse sine function:
[tex]\[
x = \sin^{-1}\left(\frac{1}{7}\right)
\][/tex]
2. Convert to Degrees: Once we have [tex]\(x\)[/tex] in radians, we convert it to degrees by multiplying by [tex]\(\frac{180}{\pi}\)[/tex]:
[tex]\[
x \text{(degrees)} = \left(\sin^{-1}\left(\frac{1}{7}\right)\right) \cdot \frac{180}{\pi}
\][/tex]
3. Round to the Nearest Tenth: Finally, we round the result to the nearest tenth of a degree.
After performing these calculations, we find that [tex]\(x \approx 8.21 \, \text{degrees}\)[/tex].
4. Select the Closest Option: Now we compare the result obtained with the given options:
- A. [tex]\(3.2^{\circ}\)[/tex]
- B. [tex]\(8.2^{\circ}\)[/tex]
- C. [tex]\(12.4^{\circ}\)[/tex]
- D. [tex]\(14.3^{\circ}\)[/tex]
The value [tex]\(8.21^{\circ}\)[/tex] rounds to [tex]\(8.2^{\circ}\)[/tex], which is option B.
Thus, the best answer is:
B. [tex]\(8.2^{\circ}\)[/tex]
