State the phase shift of y=cos(theta-[pi/3]). Then graph the function.
I know that you cannot graph on this site but how do I solve for the phase shift and to graph the phase shift, would I first have to graph the current equation?
Thanks.
when is the angle zero?
Theta-PI/3=0
at Theta=PI/3, the consine function ismax, so the phase shift is PI/3 to the LEFT.
It probably would be a good idea to graph the current equation to get the hang of it.
http://www.analyzemath.com/Graphing/GraphSineFunction.html see the shift and angle modifier explaination and example using the sin (ax+c) example
What is the phase shift of y = –csc(3x − ð)?
To determine the phase shift of the function y = cos(theta - [pi/3]), you need to compare it to the standard cosine function, y = cos(theta).
The general form of a cosine function is y = cos(theta - b), where b represents the phase shift. In this case, b is [pi/3].
Since the standard cosine function has no phase shift (b = 0), subtracting [pi/3] from theta implies a horizontal shift to the right by [pi/3] units.
To graph the function, it is helpful to have a good understanding of the general properties of the cosine function. The graph of the standard cosine function, y = cos(theta), has an amplitude of 1, a period of 2pi, and no vertical shift.
Start by plotting the known key points on the graph of the standard cosine function where theta ranges from 0 to 2pi. These points are (0, 1), (pi/2, 0), (pi, -1), (3pi/2, 0), and (2pi, 1). Connect these points smoothly with a continuous curve.
To graph the function y = cos(theta - [pi/3]), shift the entire graph to the right by [pi/3] units. This means that all the x-coordinates of the key points should be increased by [pi/3].
For example, the first key point (0, 1) will shift to ([pi/3], 1). Similarly, the second key point (pi/2, 0) will shift to ([pi/2] + [pi/3], 0), and so on. Connect these new points smoothly to create the graph of y = cos(theta - [pi/3]).
Remember, even though we cannot graph on this site, following these steps will help you visualize and understand the graph of the function.