To solve for [tex]\(\tan^{-1}(0.6316)\)[/tex], we are looking for the angle whose tangent is 0.6316.
### Step-by-Step Solution:
1. Identify the function to use:
We need the angle [tex]\( \theta \)[/tex] such that:
[tex]\[
\tan(\theta) = 0.6316
\][/tex]
2. Find the angle in radians:
Using the inverse tangent function (arctangent), we determine the angle in radians. The inverse tangent function is denoted as [tex]\( \tan^{-1} \)[/tex] or [tex]\(\arctan\)[/tex]. So,
[tex]\[
\theta = \tan^{-1}(0.6316)
\][/tex]
The angle in radians is:
[tex]\[
\theta \approx 0.5633 \text{ radians}
\][/tex]
3. Convert the angle to degrees:
To convert the angle from radians to degrees, we use the fact that:
[tex]\[
1 \text{ radian} = \frac{180}{\pi} \text{ degrees}
\][/tex]
Therefore,
[tex]\[
\theta_{\text{degrees}} = 0.5633 \times \frac{180}{\pi} \approx 32.28 \text{ degrees}
\][/tex]
In conclusion, the angle whose tangent is 0.6316 is approximately:
[tex]\[
0.5633 \text{ radians} \quad \text{or} \quad 32.28 \text{ degrees}
\][/tex]
