Question

Given that tangent squared theta = three-eighths, what is the value of secant theta? Plus-or-minus StartRoot eight-thirds EndFraction Plus-or-minus StartRoot eleven-eighths EndFraction Eleven-eighths Eight-thirds

Answer 1

Using a trigonometric identity, considering the given value of the tangent of theta, the secant of the same angle is given by:

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

How is the tangent related to the secant?

According to the following identity:

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

In this problem, the tangent squared is given as follows:

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

Hence the secant is given by:

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

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

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

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

More can be learned about trigonometric identities at https://brainly.com/question/24496175

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