# 4.6 Graphs of Other Trigonometric FUNctions - PowerPoint PPT Presentation

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4.6 Graphs of Other Trigonometric FUNctions. How can I sketch the graphs of all of the cool quadratic FUNctions?. Graph of the tangent FUNction. The tangent FUNction is odd and periodic with period π .

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4.6 Graphs of Other Trigonometric FUNctions

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## 4.6 Graphs of Other Trigonometric FUNctions

How can I sketch the graphs of all of the cool quadratic FUNctions?

### Graph of the tangent FUNction

• The tangent FUNction is odd and periodic with period π.

• As we saw in Section 2.6, FUNctions that are fractions can have vertical asymptotes where the denominator is zero and the numerator is not.

• Therefore, since, the graph of will have vertical asymptotes at , where n is an integer.

### Let’s graph y = tan x.

• The tangent graph is so much easier to work with then the sine graph or the cosine graph.

• We know the asymptotes.

• We know the x-intercepts.

### y = 2 tan (2x)

• Now, our period will be

• Additionally, the graph will get larger twice as quickly.

• The asymptotes will be at

• The x-intercept will be (0,0)

• The period is 2π.

• The asymptotes are at ±π.

• The x-intercept is (0,0).

### Graph of a Cotangent FUNction

• Like the tangent FUNction, the cotangent FUNction is

• odd.

• periodic.

• has a period of π.

• Unlike the tangent FUNction, the cotangent FUNction has

• asymptotes at period πn.

### y = cot x

• The asymptotes are at ±πn.

• There is an x-intercept at

### y = -2 cot (2x)

• The period is

• There is an x-intercept at

• There is an asymptote at

### Graphs of the Reciprocal FUNctions

• Just a reminder

• the sine and cosecant FUNctions are reciprocal FUNctions

• the cosine and secant FUNctions are reciprocal FUNctions

• So….

• where the sine FUNction is zero, the cosecant FUNction has a vertical asymptote

• where the cosine FUNction is zero, the secant FUNction has a vertical asymptote

• And…

• where the sine FUNction has a relative minimum, the cosecant FUNction has a relative maximum

• where the sine FUNction has a relative maximum, the cosecant FUNction has a relative minimum

• the same is true for the cosine and secant FUNctions

• Let’s graph y = csc x

### Now, you try your own….

• Just graph the FUNction as if it were a sine or cosine FUNction, then make the changes we have already made.

### Damped Trigonometric Graphs (Just for Fun!)

• Some FUNctions, when multiplied by a sine or cosine FUNction, become damping factors.

• We use the properties of both FUNctions to graph the new FUNction.

• For a nifty summary of the trigonometric FUNctions, please check out page 340.

• As a matter of fact, I would make sure I memorized all of the information on page 340.