Wednesday, January 9, 2013

When graphing the sine and cosine curves, remember to write the key components first, such as

Phase Shift

For example, for y = sinx and y = cosx

Amplitude = 1
Period = 2Pi
Max = 1
Min = -1
Spaces = 2Pi/4 = Pi/2
Phase shift : none
Transformation: none

The absolute value of the number in front of sin or cos is the amplitude

ex,   y = 4sinx, amplitude is 4.    y = -5cosx,  amplitude is 5

Period for both sine and cosine is 2Pi/amplitude

Max and min with no transformation is amplitude times max and amplitude times min

Spaces is the Period divided by 4

There is a phase shift if there is a + or - with the angle..

For example  y = sin(x - 1), has a phase shift of 1 to the right
                     y = sin(x + 1), has a phase shift of 1 to the left

There is a transformation if there is a + or - outside of the angle

For example, y = sinx + 2, transformation is 2 up
                     y = sinx - 2 , transformation is 2 down

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