Question

Given that tangent squared theta = three-eighths, what is the value of secant theta?

Answer 1

Answer:

$\sec \theta = \frac{\sqrt{22}}{4}$

Step-by-step explanation:

Given

$\tan^2 \theta = \frac{3}{8}$

Required

$\sec\ \theta$

We have:

$\sec^2\theta = 1 + \tan^2 \theta$

This gives:

$\sec^2\theta = 1 + \frac{3}{8}$

Take lcm and solve

$\sec^2\theta = \frac{9+3}{8}$

$\sec^2\theta = \frac{11}{8}$

Take square roots

$\sec \theta = \frac{\sqrt{11}}{\sqrt 8}$

$\sec \theta = \frac{\sqrt{11}}{2\sqrt 2}$

Rationalize

$\sec \theta = \frac{\sqrt{11}}{2\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$\sec \theta = \frac{\sqrt{22}}{4}$