To find the value of [tex]\(\sec \theta\)[/tex] given that [tex]\(\tan^2 \theta = \frac{3}{8}\)[/tex], let's follow these steps:
1. Recall the trigonometric identity:
[tex]\[
\sec^2 \theta = 1 + \tan^2 \theta
\][/tex]
2. Substitute the given value into the identity:
[tex]\[
\sec^2 \theta = 1 + \frac{3}{8}
\][/tex]
3. Simplify the expression:
[tex]\[
\sec^2 \theta = 1 + \frac{3}{8} = \frac{8}{8} + \frac{3}{8} = \frac{11}{8}
\][/tex]
4. To find [tex]\(\sec \theta\)[/tex], take the square root of both sides:
[tex]\[
\sec \theta = \pm \sqrt{\frac{11}{8}}
\][/tex]
So, the value of [tex]\(\sec \theta\)[/tex] is [tex]\(\pm \sqrt{\frac{11}{8}}\)[/tex]. Among the given options, the correct answer is:
[tex]\[
\pm \sqrt{\frac{11}{8}}
\][/tex]
