To solve the problem of finding [tex]\(\tan^{-1} 1.4826\)[/tex] to the nearest degree, follow these steps:
1. Understand the inverse tangent function ([tex]\(\tan^{-1}\)[/tex]):
The inverse tangent (or arctangent) function returns the angle whose tangent is the given number.
2. Calculate [tex]\(\tan^{-1} 1.4826\)[/tex]:
Use a calculator or a mathematical tool to find the angle in radians:
[tex]\[
\tan^{-1} 1.4826 \approx 0.9774 \text{ radians}
\][/tex]
3. Convert radians to degrees:
To convert an angle from radians to degrees, use the conversion factor [tex]\(\frac{180^\circ}{\pi} \)[/tex]:
[tex]\[
\text{Angle in degrees} = 0.9774 \times \frac{180^\circ}{\pi} \approx 56.001^\circ
\][/tex]
4. Round to the nearest degree:
Since [tex]\(56.001^\circ\)[/tex] is very close to [tex]\(56^\circ\)[/tex], we round it to the nearest whole number.
[tex]\[
\text{Rounded Degrees} = 56^\circ
\][/tex]
Therefore, the closest degree to [tex]\(\tan^{-1} 1.4826\)[/tex] is [tex]\(56^\circ\)[/tex].
Thus, the correct answer is:
b. [tex]\(56^\circ\)[/tex].
