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GeoGebra

Unit Circle to Sine and Cosine Functions

Author:L. Marizza A. Bailey, Tim Brzezinski
Creation of this resource was inspired by this resource and this resource created by Anthony Or. 1. Start with Sine. 2. Slide the bar and observe. 3. Slide the segment!, then repeat step 2. 4. Reset all the sliders. 5 Repeat steps 1 - 3 with Cosine.

What is a Sine/Cosine Graph?

Sine Graph

Which choice best fills the blank: When the point on the unit circle is at angle , the sine graph is the ______ coordinate of the point?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Cosine Graph

Which choice best fills the blank: When the point on the unit circle is at angle , the cosine graph is the ______ coordinate of the point?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

The maximum value of the Sine Graph

The sine graph reaches its maximum value when the angle is at . What is the maximum value of the sine graph (this is the y-coordinate on the sine graph)?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

The maximum value of the Cosine Graph

At what -value does the cosine reach its maximum value of 1?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Does it stop?

In the activity above, the angle doesn't pass . This is not because the graph stops, only because it was harder to make the animation keep working. What happens to the sine and cosine graph when theta passes 2π?

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