Question

Use a calculator to evaluate the expression. Express angles in radians rounded to two decimal places.

$se{c}^{-1}\left(1.4\right)$

Short answer

On evaluating the expression, we get $0.78$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$se{c}^{-1}\left(1.4\right)$

Assume$\theta =se{c}^{-1}\left(1.4\right)$.

Then,

role="math" localid="1646512392495" $$\begin{gathered} \theta =se{c}^{-1}\left(1.4\right) \\ sec\theta =1.4 \end{gathered}$$

Use the reciprocal property,

role="math" localid="1646514205969" $$\begin{gathered} sec\theta =\frac{1}{\cos \theta } \\ \frac{1}{\cos \theta }=1.4 \end{gathered}$$

Step 2. Convert into radians.

Continuing the above equation,

$$\begin{gathered} \cos \theta =\frac{1}{1.4} \\ \theta ={\cos }^{-1}\left(\frac{1}{1.4}\right) \\ \theta =44.41 \end{gathered}$$

Converting into radians,

role="math" localid="1646514476368" $$\begin{gathered} \theta =44.41\left(\frac{\mathrm{\pi }}{180}\right) \\ =0.7751 \end{gathered}$$

Rounding off to two decimal places,

$\theta =0.78$