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Inverse Trig Functions. Learning Goals: Understand Domain/Range requirements for inverse trig functions Be able to calculate exact values for inverse trig functions. Understand the composition of inverse trig functions Be able to calculate compositions with inverse trig functions.

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inverse trig functions

Inverse Trig Functions

Learning Goals:

Understand Domain/Range requirements for inverse trig functions

Be able to calculate exact values for inverse trig functions.

Understand the composition of inverse trig functions

Be able to calculate compositions with inverse trig functions.

find exact values
Find Exact Values
  • Get out that plate!
  • What is the angle whose sine is ½ ?
  • Arcsin( ½ ) = θ or sin-1( ½ ) = θ
  • What is the angle whose cosine is ½ ?
  • Arccos( ½ ) = θ or cos-1( ½ ) = θ
  • Are there other angles whose sine is ½ ?
  • Are there other angles whose cosine is ½?
trigonometric values of common angles
Trigonometric Values of Common Angles

y

(0, 1)

90°

60°

120°

135°

45°

30°

150°

x

180°

360°

(–1, 0)

(1, 0)

210°

330°

315°

225°

240°

300°

270°

(0, –1)

Unit Circle

Angles

and

Coordinates

Everything shows up on

the next click.

summary from sketchpad
Summary from Sketchpad
  • With no restrictions, inverses of sin, cos and tangent are not functions.
  • With restrictions:
  • Arcsin(x) = θ
  • Domain: {x|-1 ≤ x ≤ 1}
  • Range:{θ| -π/2≤ θ ≤ π/2}
  • Arccos(x) = θ
  • Domain: {x|-1 ≤ x ≤ 1}
  • Range: {θ|0 ≤ θ ≤ π}
  • Arctan(x) = θ
  • Domain: {x|x єR}
  • Range: :{θ| -π/2≤ θ ≤ π/2}
so what
So what?
  • Q: What are you supposed to get out of knowing and understanding these domain restrictions?
  • A: I hate answering questions on powerpoint slides. You give me the answer.
compositions
Compositions
  • Y = sin x is the inverse of y = arcsin(x).
  • So what is sin(arcsin(x))?
  • Arcsin(sin(x))?
  • See if you can find an example when these compositions wouldn’t work.
practice time
Practice Time
  • Use your unit circle to do problems from the book: p. 465
trigonometric values of common angles9
Trigonometric Values of Common Angles

y

(0, 1)

90°

60°

120°

135°

45°

30°

150°

x

180°

360°

(–1, 0)

(1, 0)

210°

330°

315°

225°

240°

300°

270°

(0, –1)

Unit Circle

Angles

and

Coordinates

Everything shows up on

the next click.