Chapter 7, Problem 8CT

To determine

The solution of ${\sec }^{-1}1.4$ using calculator. Express answer in radian rounded to two decimal places.

Answer to Problem 8CT

Solution:

The solution of ${\sec }^{-1}1.4$ using calculator is $0.78$.

Explanation of Solution

Given information:

The expression, ${\sec }^{-1}1.4$

Explanation:

The expression ${\sec }^{-1}1.4$ can be written as ${\cos }^{-1}\left(\frac{1}{1.4}\right)$

$\Rightarrow {\cos }^{-1}\left(\frac{1}{1.4}\right)={\cos }^{-1}\left(0.7142857143\right)$

Use the steps below to find solution of ${\cos }^{-1}\left(0.7142857143\right)$ using calculator. First set the calculator to radian mode.

Step I: Press the ON key.

Step II: Press the SHIFT or $2^{\text{nd}}$ key.

Step III: Press the “cos” on the same calculator.

Step IV: Enter $0.7142857143$ then complete the parenthesis.

Step V: Press enter button.

The screen shows the answer $0.7751933733$.

Round $0.7751933733$ to two decimal places get $0.78$

Therefore, the solution of ${\sec }^{-1}1.4$ using calculator is $0.78$ radian.