Pre-Calculus 12 Notes

By: Gen L.

Lesson 2: The Unit Circle

Unit Circle

• Radius
• Centered at the Origin
• Equation of the unit circle:

Circle Equations

• Centered at Origin, radius
• Example: radius 5

• Centered not at origin. Like translating a function.
• Example: radius 5, center

Points on Unit Circle

• Determine the y-value on unit circle when
  • (Always start here when finding points.)

Points on Unit Circle

• Is the point on the unit circle? ()
• Let's see:
• So, is
  
  
  
  

Arclength

• Remember the arclength formula ()?
• For the unit circle, since r = 1, (in radians)

Coordinates of Angled Lines

• Determine coordinates of all points where the terminal arm of is represented by .
• Assumptions:
  • , .

Angled Lines, cont.

• ,
• ,
• , .
• Wait, this looks familiar...

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