6.8 – Trig Inverses and their graphs

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# 6.8 – Trig Inverses and their graphs - PowerPoint PPT Presentation

6.8 – Trig Inverses and their graphs . Quick Review. How do you find inverses of functions? Are inverses of functions always functions? How did we test for this?. Inverse Trig Functions. Consider the graph of y = sin x. What is the domain and range of sin x?

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## 6.8 – Trig Inverses and their graphs

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### 6.8 – Trig Inverses and their graphs

Quick Review
• How do you find inverses of functions?
• Are inverses of functions always functions?
• How did we test for this?
Consider the graph of y = sin x
• What is the domain and range of sin x?
• What would the graph of y = arcsin x look like?
• What is the domain and range of arcsin x?

Domain: all real numbers

Range: [-1, 1]

Domain: [-1, 1]

Range: all real numbers

Is the inverse of sin x a function?
• This will also be true for cosine and tangent.
• Therefore all of the domains are restricted in order for the inverses to be functions.
• Capital letters are used to distinguish when the function’s domain is restricted.
Table of Values of Sin x and Arcsin x

Why are we using these values?

Table of Values of Cos x and Arccos x

Why are we using these values?

Table of Values of Tan x and Arctan x

Why are we using these values?

Write an equation for the inverse of y = Arctan ½x. Then graph the function and its inverse.
• To write the equation:
• Exchange x and y
• Solve for y

Let’s graph 2Tan x = y first.

Complete the table:

Then graph!

• x = Arctan ½y
• Tan x = ½y
• 2Tan x = y

Now graph the original function, y = Arctan ½x by switching the table you just completed!

Write an equation for the inverse of y = Sin(2x). Then graph the function and its inverse.
• To write the equation:
• Exchange x and y
• Solve for y

Let’s graph y = Sin(2x)first.

Why are these x-values used?

• x = Sin(2y)
• Arcsin(x) = 2y
• Arcsin(x)/2 = y

Now graph the inverse function, y = Arcsin(x)/2 by switching the table you just completed!