To find the approximate value of [tex]\(\tan 38^\circ\)[/tex], follow these steps:
1. Convert the angle from degrees to radians: Most trigonometric functions on calculators require the angle to be in radians. The formula to convert degrees to radians is:
[tex]\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\][/tex]
Plugging in our angle:
[tex]\[
\text{radians} = 38^\circ \times \frac{\pi}{180} \approx 0.6632 \text{ radians}
\][/tex]
2. Calculate the tangent of the angle in radians: Use the tangent function on the calculator, which typically requires input in radians.
[tex]\[
\tan 0.6632 \approx 0.7813
\][/tex]
So, the approximate value of [tex]\(\tan 38^\circ\)[/tex], rounded to 4 decimal places, is:
[tex]\[
\tan 38^\circ \approx 0.7813
\][/tex]
Thus, [tex]\(\tan 38^\circ\)[/tex] is approximately [tex]\(\boxed{0.7813}\)[/tex].
