How do you use $tan θ = 4$ $tantheta=4$ to find $sec θ$ $sectheta$ ?

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Answer 1 · 2017-01-23T19:15:18

Use the identity $sec (θ) = \pm \sqrt{1 + {tan}^{2} (θ)}$ $sec(theta) = +-sqrt(1 + tan^2(theta))$

Given: $tan (θ) = 4$ $tan(theta) = 4$

Substitute ${(4)}^{2}$ $(4)^2$ for ${tan}^{2} (θ)$ $tan^2(theta)$ into the identity:

$sec (θ) = \pm \sqrt{1 + 4^{2}}$ $sec(theta) = +-sqrt(1 + 4^2$

$sec (θ) = \pm \sqrt{17}$ $sec(theta) = +-sqrt17$

Whether the secant is positive or negative cannot be determined with the given information.

How do you use tantheta=4tanθ=4tantheta=4 to find secthetasecθsectheta?