Chapter 12, Problem 6CT

To determine

Find the value of $\sec 145.8°$ .

Answer to Problem 6CT

The value of $\sec 145.8°$ is $-1.209$ .

Explanation of Solution

Given information: The given trigonometric function is $\sec 145.8°$ .

Calculation: Evaluate $\sec 145.8°$ ,

  $\sec 145.8°=-1.209$

Hence the value of $\sec 145.8°$ is $-1.209$ .

To determine

If $\cos \theta =0.5606\text{ and 9}0°\text{<}\theta <360°$ then find the value of $\left(\theta \right)$ .

Answer to Problem 6CT

The value of $\left(\theta \right)$ is $304.1°$ .

Explanation of Solution

Given information: It is given that $\cos \theta =0.5606\text{ and 9}0°\text{<}\theta <360°$ .

Calculation: Evaluate for $\cos \theta =0.5606\text{ and 9}0°\text{<}\theta <360°$ ,

  $\begin{array}{c}\cos \theta =0.5606\\ \theta ={\cos }^{-1}\left(0.5606\right)\\ \theta =55.9°\end{array}$

Since the angle $\left(\theta \right)$ lies in between second and fourth quadrant and obtained value of $\left(\theta \right)$ is $55.9°$ . Therefore subtract $55.9°$ from $360°$ .

  $\begin{array}{c}\theta =360°-55.9°\\ =304.1°\end{array}$

Hence the value of $\left(\theta \right)$ is $304.1°$ .