All Trigonometry Resources
Example Questions
Example Question #1 : Phase Shifts
Identify the phase shift of the following equation.
If we use the standard form of a sine function
the phase shift can be calculated by
. Therefore, in our case, our phase shift is
Example Question #1 : Phase Shifts
Which of the following is equivalent to
The first zero can be found by plugging 3π/2 for x, and noting that it is a double period function, the zeros are every π/2, count three back and there is a zero at zero, going down.
A more succinct form for this answer is
but that was not one of the options, so a shifted cosine must be the answer.The first positive peak is at π/4 at -1, so the cosine function will be shifted π/4 to the right and multiplied by -1. The period and amplitude still 2, so the answer becomes
.To check, plug in π/4 for x and it will come out to -2.
Example Question #132 : Trigonometry
Which of the following is the correct definition of a phase shift?
The distance a function is shifted vertically from the general position
The distance a function is shifted horizontally from the general position
The distance a function is shifted diagonally from the general position
A measure of the length of a function between vertical asymptotes
The distance a function is shifted horizontally from the general position
Take the function
for example. The graph for is
If we were to change the function to
, our phase shift is . This means we need to shift our entire graph units to the left.
Our new graph
is the following
Example Question #12 : Trigonometric Graphs
Consider the function . What is the phase shift of this function?
The general form for the secant transformation equation is
. represents the phase shift of the function. When considering we see that . So our phase shift is and we would shift this function units to the left of the original secant function’s graph.
Example Question #13 : Trigonometric Graphs
True or False: If the function has a phase shift of , then the graph will not be changed.
False
True
Example Question #2 : Phase Shifts
Which of the following is the graph of
with a phase shift of ?Start this problem by graphing the function of tangent.
Now we need to shift this graph
to the right.This gives us our answer
Example Question #1 : Phase Shifts
True or False: The function has a phase shift of .
True
False
False
The form of the general cosecant function is . So if we have then , which represents the phase shift, is equal to . This gives us a phase shift of .
Example Question #61 : Trigonometric Functions And Graphs
Which of the following is the phase shift of the function ?
The general form of the cotangent function is
. So first we need to get into the form .
From this we see that giving us our answer.