# trigonometric graph

• Sep 25th 2008, 05:03 PM
trigonometric graph
1. The curve above is the graph of a sinusoidal function. It goes through the point http://webwork.math.wvu.edu/webwork2...3163a76b21.png and http://webwork.math.wvu.edu/webwork2...665cb877b1.png. Find a sinusoidal function that matches the given graph. If needed, you can enter http://webwork.math.wvu.edu/webwork2...06b3a9b1d1.png=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

http://webwork.math.wvu.edu/webwork2...rob1image1.png

2.The curve above is the graph of a sinusoidal function. It goes through the points http://webwork.math.wvu.edu/webwork2...d970baf041.png and http://webwork.math.wvu.edu/webwork2...087b3dbdf1.png. Find a sinusoidal function that matches the given graph. If needed, you can enter http://webwork.math.wvu.edu/webwork2...06b3a9b1d1.png=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

http://webwork.math.wvu.edu/webwork2...rob2image1.png
• Sep 25th 2008, 05:28 PM
skeeter
1. looks like a -sine curve

amplitude = 3
period = 6
phase shift = none
vertical shift = +3

$y = -3sin\left(\frac{\pi}{3}x\right) + 3$

2. I'd use a cosine curve for this one ...

amplitude = 4
period = 6
phase shift = left 2
vertical shift = none

you try it.
• Sep 25th 2008, 05:34 PM
Nobby
changing the sine function
You need to find a solution of the form

A + B sin (Cx - D)

where A shifts the wave up, here A = 3 as the wave moves around +3

B gives the size up and down, if B = 1 we have a size of 2, so we want B = 3 as we have a size of 6

C controls the period, a normal wave is period 2 pi, we want period 6, so C = pi/3

D controls the shift to the right, we actually want the shift to the left so that Cx - D = 0 when x = -3 hence D = -pi
$
y = 3 + 3sin\left(\frac{\pi}{3}x + \pi\right)
$

hope this helps you do the second question on your own.

cheers

Nobby
• Sep 25th 2008, 06:04 PM
$y = 4\cos\left[\frac{\pi}{3}(x + 2)\right]$