1. Section 3.5 Cosecant Secant and Cotangent Functions
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2. i) Review: Reciprocal Functions
The reciprocal function takes the reciprocal of all the y-coordinates of a function
When graphing a reciprocal function, there are a three main steps:
The reciprocal of 1 or -1 will be the same, so points with a y-coordinate of 1 will not change
The reciprocal of zero is undefined, so points with a y-coordinate of zero will become a vertical asymptote
Take the reciprocal of all y-coordinates to find where the points of the new function is.
Reciprocal of large numbers become small
Reciprocal of small numbers become large
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3. Practice: Given the following Function, graph the reciprocalx y -5 5
Find the x-intercept  Vertical Asymptote
Find common points with a
Y-coordinate of 1 or -1
Pick some points on the original
Function and take the reciprocal
of the Y-coordinate
Reciprocal of large numbers will become small
Reciprocal of small numbers
Will become large
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4. II) Reciprocal of Trigonometric Functions
Cosecant is the reciprocal of the sine function
Secant is the reciprocal of the cosine function
Cotangent is the reciprocal of the tangent function
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5. Ex: Determine the value of each expression to 3 decimal places

6. III) Graphing Cosecant Functionx y p 2p 3p 4p 5p -2 2
When sinθ=0 , you will get Vertical Asymptotes
When sinθ=1 or -1, you will get Common points
Take the reciprocal of each sub-domain
Y-coordinates are large  Reciprocal will be small
Y-coordinates are small  Reciprocal will be large
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7. IV) Graphing Secant Functionx y p 2p 3p 4p 5p -2 2
When cosθ=0 , you will get Vertical Asymptotes
When cosθ=1 or -1, you will get Common points
Take the reciprocal of each sub-domain
Y-coordinates are large  Reciprocal will be small
Y-coordinates are small  Reciprocal will be large
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8. V) Graphing Cotangent Functionx y p 2p 3p 4p 5p -2 2
V.A. from tanθ will become x-intercepts
When tanθ=0 , you will get Vertical Asymptotes
When tanθ=1 or -1, you will get Common points
Y-coordinates are large  Reciprocal will be small
Y-coordinates are small  Reciprocal will be large
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9. Ex: Indicate the Domain & Range for each of the following functions:y p 2p 3p 4p -2 2 x y p 2p 3p 4p -2 2 x y p 2p 3p 4p -2 2

10. Ex: Solve for θ in each of the following:
Take the reciprocal
of both sides
Take the reciprocal
of both sides
The ratio is positive
The ratio is negative

12. Homework:
Assignment 3.5