6 8 trig inverses and their graphs n.
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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?. Inverse Trig Functions. Consider the graph of y = sin x. What is the domain and range of sin x?

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Presentation Transcript
quick review
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
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
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.
how do you know if the domain is restricted for the original functions
How do you know if the domain is restricted for the original functions?
  • Capital letters are used to distinguish when the function’s domain is restricted.
table of values of sin x and arcsin x
Table of Values of Sin x and Arcsin x

Why are we using these values?

table of values of cos x and arccos x
Table of Values of Cos x and Arccos x

Why are we using these values?

table of values of tan x and arctan x
Table of Values of Tan x and Arctan x

Why are we using these values?

write an equation for the inverse of y arctan x then graph the function and its inverse
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
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!