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: RadiansDegreesNotes The Period 2π2π360 The amplitude 11 The coordinates of the starting point aka Y-intercept (0,0) Sine “starts” in the middle and increases) key point #1 The maximum (90, 1)Key point #2 Second x intercept (180,0)Key point #3 The minimum point (270, -1)Key point # 4 End point (3 rd x-intercept) (360, 0)Key point #5

Critical values of the parent graph of the cosine function: RadiansDegreesNotes The Period 2π2π360 The amplitude 11 The coordinates of the starting point aka Y-intercept Aka the maximum (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!

All at once but more than once!