Sunday, October 23, 2011

Practice for graphing sine waves.


If you want to visualize the graphs you are asked to draw, the website Wolfram|Alpha has an instruction you can type called "plot". Here is the example of plot 3sin(2x/3).

Here are some examples for practice without graphs. You can do that yourself on Wolfram|Alpha. The answers are in the comments.

a] f(x) = 2 + 4sin(x/2)

period = ______

amplitude = _______

maximum of f is ______, reached when x = _______.


minimum of f is ______, reached when x = _______.

b] k(x) = 4 + 2cos(3x)

period = ______

amplitude = _______

maximum of k is ______, reached when x = _______.

minimum of k is ______, reached when x = _______.

c] q(x) = 1 - 3sin(5x)

period = ______

amplitude = _______

maximum of q is ______, reached when x = _______.

minimum of q is ______, reached when x = _______.

Answers in the comments.

1 comment:

  1. a] f(x) = 2 + 4sin(x/2)


    period = 2pi/(1/2) = 4pi.


    amplitude = 4.

    Sine reaches max when x = pi/2, but the function is sin(x/2), so x/2 = pi/2 when x = pi. The value will be 2 + 4 = 6.


    maximum of f is 6, reached when x = pi.

    There are other values of x where f(x) = 6.



    Sine reaches min when x = -pi/2 or 3pi/2, but the function is sin(x/2), so x/2 = -pi/2 when x = -pi or x/2 = 3pi/2, so x = 3pi. The value will be 2 - 4 = -2.


    minimum of f is -2, reached when x = -pi.


    minimum of f is -2, reached when x = 3pi.

    There are other values of x where f(x) = -2.


    b] k(x) = 4 + 2cos(3x)


    period = 2pi/3


    amplitude = 2

    Cosine reaches a maximum when x = 0, so k(0) = 4 + 2 = 6. It also reaches a max at x = 2pi, so 3x = 2pi when x = 2pi/3


    maximum of k is 6, reached when x = 0.


    maximum of k is 6, reached when x = 2pi/3.


    Cosine reaches its minimum at -pi or pi, among other values, and that minimum will be 4 - 2 = 2. This happens at x = pi/3 or x = -pi/3.


    minimum of k is 2, reached when x = pi/3.

    minimum of k is 2, reached when x = -pi/3.



    c] q(x) = 1 - 3sin(5x)


    period = 2pi/5


    amplitude = 3

    Because sine is multiplied by -3, q(x) will reach a minimum when sin(5x) = 1 and a maximum when sin(5x) = -1. The lowest value is 1 - 3 = -2 and the highest value is 1 + 3 = 4.


    maximum of q is 4, reached when x = pi/10.

    maximum of q is 4, reached when x = -3pi/10.



    minimum of q is -2, reached when x = 3pi/10.


    minimum of q is -2, reached when x = -pi/10.

    ReplyDelete