Graphing Sine and Cosine Functions

Hey everyone!!
I'm going to try and explain graphing sine & cosine functions to you and hopefully it helps!!

Here are some points that will be helpful to understand graphing sine and cosine functions.

• Graphing on a Cartesian plane is known as "unrolling" the Unit Circle.
• Plot theta values on the x-axis and the trigonometric function values at theta on the y-axis
• One cycle is a portion of the graph from one point to another at which time the graph begins to repeat itself.
• One period is the length of one cycle in either degrees or radians. The period for a sin x or cos x function is 2pi/[b]. The period for a tan x function is pi/[b].
• The amplitude is the distance from the middle axis to the highest or lowest point for a sin x or cos x function. A change in amplitude vertically stretches or compresses the basic shape of the curve. The amplitude for sin x of cos x function is (a).  The amplitude for a tan x function is unlimited or infinite

                 Amplitude= max-min/2 

• Basic equations: y = a sin bx and y = a cos bx 
• X represents theta values and y represents the trigonometric function's value at theta.

Examples:

This problem is a combination of dealing with the values of A and B.  The A value of 3 tells us that the graph will have a vertical stretch and the amplitude will be 3.  The B value of 1/2 tells us that a complete cycle of the graph will require more than the standard domain of  0 to (there will be a horizontal stretch).
The period of this new graph will be (or 720º).

 

This problem is also a combination of dealing with the values of A and B.  The A value of 1/2 tells us that the graph will have a vertical shrink and an amplitude of 1/2.  The B value of 3 tells us that 3 complete cycles of the graph will be seen in the standard domain of  0 to (there will be a horizontal shrink).
The period of this new graph will be (or 120º).

 

 

 I hope this helps anyone if someone is struggling!! See you guys in class :)