Final answer:
To label the period, frequency, and phase shift for the function y=2+sec(theta+3pi/4), the period is 2pi, the frequency is 1/2pi, and the phase shift is 3pi/4. The graph can be obtained by shifting the graph of y=2+sec(theta) right by 3pi/4 units, and the first period is highlighted by using the range of theta from 0 to 2pi.
Step-by-step explanation:
To label the period, frequency, and phase shift for the equation y=2+sec(theta+3pi/4), we can rewrite it as y=2+sec(theta+(3pi/4)).
The period of sec(theta) is 2pi, so the period of sec(theta+(3pi/4)) is also 2pi.
The frequency is the reciprocal of the period, so the frequency is 1/2pi.
The phase shift is the value inside the parentheses in the equation, so the phase shift is 3pi/4.
To graph the equation, we can start by graphing y=2+sec(theta) and then shift the graph right by 3pi/4 units.
Highlighting the first period, we can use the range of theta from 0 to 2pi.