Question #c1993

Question

1267 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-04T22:20:18

Many calculators don't have a ${sec}^{- 1}$ $sec^-1$ button. So, if we want to evaluate ${sec}^{- 1} (8)$ $sec^-1(8)$ , we'll have to rewrite it.

First, let:

${sec}^{- 1} (8) = θ$ $sec^-1(8)=theta$

Via the definition of inverse functions:

$8 = sec (θ)$ $8=sec(theta)$

Since secant and cosine are reciprocals:

$\frac{1}{8} = cos (θ)$ $1/8=cos(theta)$

Then:

${cos}^{- 1} (\frac{1}{8}) = θ$ $cos^-1(1/8)=theta$

Thus:

${sec}^{- 1} (8) = {cos}^{- 1} (\frac{1}{8})$ $sec^-1(8)=cos^-1(1/8)$

Which can be plugged into a calculator.