Graphs of Functions
y = sin(x) and y = cos(x)
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center


Graphs of trigonometric functions can be produced in degrees or in radians.
The graphs appearing here will be done in radians.

Hint:  When hand-drawing the graphs of sine and cosine, draw vertical dotted lines at  intervals to remind you of the connection to the quadrants from the unit circle and to keep your graphs accurate.  (Such dotted lines will resemble the dashed vertical grid lines in the graphs below.)

 

The sine and cosine functions take on y-values between -1 and 1. 

Sine Function:  
     called a "wave" because of its rolling wave-like
          appearance (also referred to as oscillating)
     amplitude: 1  (height)
    period:    (length of one cycle)
   
frequency:  1 cycle in radians [or 1/()]
   
domain: 
   
range:   

At x = 0, the sine wave is on the shoreline!
(meaning the y-value is equal to zero)



 

Cosine Function:      
    called a "wave" because of its rolling wave-like
          appearance
     amplitude: 1
    period: 
   
frequency:  1 cycle in radians [or 1/()]
   
domain: 
   
range:   

At x = 0, the cosine wave breaks off the cliff!
(meaning the y-value is equal to one)

 

Did you notice that the cosine curve is really the exact same graph as the sine curve shifted 90 (or radians) to the left!

 

How to use your
TI-83+/84+ graphing calculator for graphing trig functions.
Click calculator.