Trigonometric Graphs (all six) - Pre-Calculus

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 .

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 .

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 .

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

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 .

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 .

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 .

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.

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.

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 .

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 .

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

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 .

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)

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 .

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 .

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 .

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.

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.