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