4.6 Graphs of Other Trigonometric FUNctions

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# 4.6 Graphs of Other Trigonometric FUNctions - PowerPoint PPT Presentation

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

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