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Parent graphs of sine and cosine
Key features and critical values
Unit circle to graph
• Let the animation run on the next slide to see how the graphs of all 6 functions relate to a point rotating around the unit circle.
Sine and cosine and the unit circle
• See the site below for cool demonstration of the sine graph, cosine graph, or tangent graph as it relates to a point rotating around the unit circle.
• This site gives a clearer picture then the previous demo.
• Simulation of sine and cosine graphs
Angles: the unit circle and graphs
A moment to define how we describe and measure angles.
• ray is the ray that an angle starts from.• Terminal ray is the ray that an angle ends on.• A revolution is one complete circular motion.
Angles in standard position
• The vertex of the angle is on (0,0).• Initial ray starts on the positive x-axis• The angle is measure counter clockwise.• The terminal ray can be in any of the
quadrants.
Graphing with the 5 key points
• 1 complete period of Sine or Cosine can be graphing using the 5 key points.
• For each specific equation, the horizontal spacing between each point is constant. i.e. if it is 3 units between point 2 to point 3, then it is also 3 unit between point 4 and point 5.
• For both sine and cosine, the 5 key points will always be; maximum values, minimum values, and points on the axis of the wave.
• the axis of the wave for the parent graphs is the X-axis.
Critical values of sine and cosine
• A blank copy of the grid is one of the links on my blog.
• Copy the charts below onto that, or simply print these slides full page.
Critical values of the parent graph of the sine function:
Radians Degrees NotesThe Period 2π 360
The amplitude 1 1
The coordinates of the starting pointaka Y-intercept
(0,0) (0,0) Sine “starts” in the middle and increases) key point #1
The maximum (90, 1) Key point #2
Second x intercept (, 0) (180,0) Key point #3
The minimum point ( (270, -1) Key point # 4
End point (3rd x-intercept) ( (360, 0) Key point #5
Critical values of the parent graph of the cosine function:Radians Degrees Notes
The Period 2π 360
The amplitude 1 1
The coordinates of the starting pointaka Y-intercept Aka the maximum
(0,1) (0,1) cosine “starts” at the maximum and decreases key point #1
The first x-intercept (90, 0) Key point #2
The minimum point ( (180,-1) Key point #3
The second x intercept ( (270, 0) Key point # 4
End point (back to max) ( (360, 1) Key point #5
All at once!
x
y
-1
0
1
GREEN is sine
Blue is cosine
All at once but more than once!
x
y
-1
0
1