DAY 18
Graphs of Sine and Cosine Curve
THE SINE WAVE
Fill out the tables and graph the function:
0
.707
1
.707
0
-.707
-1
-.707
0
.707
1
THE COSINE WAVE
Fill out the tables and graph the function:
1
.707
0
-.707
-1
-.707
0
.707
1
.707
0
HOW ARE DEGREES AND RADIANS
RELATED?
The easiest ratio to remember is 180° is equal to π.
So convert the following:
45 ° to radians .785, we would write this as 1/4π or π/4 because 45/180 = 1/4
90 ° to radians 1.57, 1/2π or π/2
135 ° to radians 2.36, 3/4π or 3π/4
225 ° to radians 3.93, 5/4π or 5π/4
270 ° to radians 4.71, 3/2π or 3π/2
315 ° to radians 5.34, 7/4π or 7π/4
360 ° to radians 6.28, 2π
CHARACTERISTICS OF SINE AND COSINE
WAVES
• Sine and Cosine functions are called periodic
functions. This is because it is a function that repeats
y-values in a cycle.
• Period: horizontal length of one cycle.
• Amplitude: half the difference between the
maximum and minimum values of the function.
NAME THE TYPE OF WAVE, PERIOD, AND
AMPLITUDE OF THE FOLLOWING EXAMPLES:
• Sine
• Cosine
• Period: 0 to π
• Period: 0 to 2π
• Amplitude: 3
• Amplitude: 4
• Sine
• Period:0 to 2π
• Amplitude: 2
• Cosine
• Period: 0 to 2π
• Amplitude: 5
FINDING PERIOD AND AMPLITUDE FROM
THE EQUATION
Type the following function into your calculator and determine the
period and amplitude. Hit ZOOM 6 first then… MAKE SURE IN YOUR
WINDOW SETTING THE XSCL is 1/2π.
Group 1: y = sin4x
Group 5: y = 2sin(-4x)
Group 2: y = cos5x
Group 6: y = 3 sin(2/3x)
Group 3: y = 4cosx
Group 7: y = -4 cos5x
Group 4: y = -2sinx
Group 8: y = 3cos(-2x)
Group 9: y = 3sinx
HOW IS THE PERIOD AND AMPLITUDE
RELATED TO THE EQUATION?
Group 1: y = sin4x
P:0 to 1/2π
A: 1
to 1/2π
Group 5: y = 2sin(-4x) P:0
A: 2
Group 2: y = cos2x
P:0 to π
A: 1
to 3π
Group 6: y = 3sin(2/3x)P:0
A: 3
Group 3: y = 4cosx
P:0 to 2π
A: 4
Group 7: y = -4 cos2x
Group 4: y = -2sinx
P:0 to 2π
A: 2
to π
Group 8: y = 3cos(-2x)P:0
A: 2
Group 9: y = 3sinx
P:0 to π
A: 4
P:0 to 2π
A: 3
Period = 2π/ | # next to x|
Amplitude = | # out front|