# Precalculus : Trigonometric Graphs (all six)

## Example Questions

### Example Question #1 : Trigonometric Graphs (All Six)

Which of the trigonometric functions is represented by this graph?

y = sec x

y = csc x

y = tan x

y = cot x

y = csc x

Explanation:

This graph is the graph of y = csc x. The domain of this function is all real numbers except  where n is any integer. In other words, there are vertical asymptotes at all multiples of . The range of this function is . The period of this function is .

### Example Question #112 : Graphing Functions

Which of the following functions is represented by this graph?

y = sec x

y = cot x

y = tan x

y = csc x

y = cot x

Explanation:

This graph is the graph of y = cot x. The domain of this function is all real numbers except  where n is any integer. In other words, there are vertical asymptotes at all multiples of . The range of this function is . The period of this function is .

### Example Question #113 : Graphing Functions

Which of the following functions is represented by this graph?

y = cot x

y = csc x

y = tan x

y = sec x

y = sec x

Explanation:

This graph is the graph of y = sec x. The domain of this function is all real numbers except  where n is any integer. In other words, there are vertical asymptotes at  , , and so on. The range of this function is . The period of this function is

### Example Question #1 : Trigonometric Graphs (All Six)

Which of the following functions is represented by this graph?

y = sec x

y = csc x

y = tan x

y = cot x

y = tan x

Explanation:

This graph is the graph of y = tan x. The domain of this function is all real numbers except  where n is any integer. In other words, there are vertical asymptotes at , and so on. The range of this function is . The period of this function is .

### Example Question #5 : Trigonometric Graphs (All Six)

Which of the following functions has a y-intercept of

Explanation:

The y-intercept of a function is found by substituting . When we do this to each, we can determine the y-intercept. Don't forget your unit circle!

Thus, the function with a y-intercept of  is

### Example Question #1 : Trigonometric Graphs (All Six)

Which of the following functions is represented by this graph?

y = csc(x)

y = tan(x)

y = sec(x)

y = cos(x)

y = sin(x)

y = cos(x)

Explanation:

This graph is the graph of y = cos x. The domain of this function is all real numbers. The range of this function is . The period of this function is .

### Example Question #122 : Graphing Functions

Which of the following functions is represented by this graph?

y = csc x

y = sin x

y = cos x

y = sec x

y = tan x

y = sin x

Explanation:

This graph is the graph of y = sin x. The domain of this function is all real numbers. The range of this function is . The period of this function is .

### Example Question #8 : Trigonometric Graphs (All Six)

True or false: If you translate a secant function  units to the left along the x-axis, you will have a cosecant curve.

True

False

False

Explanation:

This is false. While the graphs of secant and cosecant functions are related, in order to turn a secant function into a cosecant function, you'd need to translate the original graph  units to the right to obtain a cosecant graph.

### Example Question #2 : Trigonometric Graphs (All Six)

Where does the tangent function intercept the x-axis?

x= all real numbers

No solution

Explanation:

Because the tangent function is periodic, it intercepts the x-axis in infinitely many places. We can see several of these in the graph below:

In the photo, we can see that the function is intercepting the x-axis at  Generalizing this, we can say that the tangent function intercepts the x-axis for  for all values of n such that n is an integer.

### Example Question #123 : Graphing Functions

True or false: If you translate a sine curve 90o to the left along the x-axis, you will have a cosine curve.

False

True

True

Explanation:

This is true! Notice the similarity of the shape between the graphs, but that they intercept the x-axis at different spots, and their peaks and valleys are at different spots.

y=sin(x), passes through the point (0,0)

y=cos(x), passes through the point (0,1)