### All Trigonometry Resources

## Example Questions

### Example Question #1 : Phase Shifts

Identify the phase shift of the following equation.

**Possible Answers:**

**Correct answer:**

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 #2 : Phase Shifts

Which of the following is equivalent to

**Possible Answers:**

**Correct answer:**

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 #3 : Phase Shifts

Which of the following is the correct definition of a phase shift?

**Possible Answers:**

The distance a function is shifted horizontally from the general position

A measure of the length of a function between vertical asymptotes

The distance a function is shifted vertically from the general position

The distance a function is shifted diagonally from the general position

**Correct answer:**

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 #4 : Phase Shifts

Consider the function . What is the phase shift of this function?

**Possible Answers:**

**Correct answer:**

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 #5 : Phase Shifts

True or False: If the function has a phase shift of , then the graph will not be changed.

**Possible Answers:**

True

False

### Example Question #6 : Phase Shifts

Which of the following is the graph of with a phase shift of ?

**Possible Answers:**

**Correct answer:**

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 #7 : Phase Shifts

True or False: The function has a phase shift of .

**Possible Answers:**

False

True

**Correct answer:**

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 #8 : Phase Shifts

Which of the following is the phase shift of the function ?

**Possible Answers:**

**Correct answer:**

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.

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