Chapter 7.7, Problem 35E

To determine

To graph: the given function.

Explanation of Solution

Given information:

  $y=\csc \left(\theta +60°\right)$

Calculation:

The given function is in the form of $y=A\csc \left(kx+c\right)$ . Compare the given function with the cosine function to get $x=\theta ,A=1,k=1$ and $c=60°$ . The amplitude and period of function is evaluated as shown below.

  $\begin{array}{c}\text{Amplitude}=\left|A\right|\\ =\left|1\right|\left[\text{Put the value of }A\right]\\ =1\end{array}$

The period of function is evaluated as shown below.

  $\begin{array}{c}\text{Period}=\frac{2\pi }{k}\\ =\frac{2\pi }{1}\left[\text{Put the value of }k\right]\\ =2\pi \end{array}$

The phase shift of the function is evaluated as follows:

  $\begin{array}{c}\text{Phase shift}=-\frac{c}{k}\\ =-\frac{60°}{1}\left[\text{Put the value of }k\text{ and }c\right]\\ =-\frac{60°}{1}\left(\frac{\pi }{180°}\right)\left[\text{Convert into radians}\right]\\ =-\frac{\pi }{3}\end{array}$

Now use this information to plot the coordinates on the graph and connect them with a smooth curve as shown below.