Question

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

Answer 1

answer is B

Explanation:

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Answer 2

`\sec \theta = (√(22))/(4)`

Explanation:

Given

`\tan^2 \theta = (3)/(8)`

Required

`\sec\ \theta`

We have:

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

This gives:

`\sec^2\theta = 1 + (3)/(8)`

Take lcm and solve

`\sec^2\theta = (9+3)/(8)`

`\sec^2\theta = (11)/(8)`

Take square roots

`\sec \theta = (√(11))/(\sqrt 8)`

`\sec \theta = (√(11))/(2\sqrt 2)`

Rationalize

`\sec \theta = (√(11))/(2\sqrt 2) * (\sqrt 2)/(\sqrt 2)`

`\sec \theta = (√(22))/(4)`