1. ## trigonometric graph

1. The curve above is the graph of a sinusoidal function. It goes through the point and . Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

2.The curve above is the graph of a sinusoidal function. It goes through the points and . Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

2. 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.

3. ## 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

4. for question 2..i got 4cos(pi/3) but i dont know what to do for phase shift

5. $y = 4\cos\left[\frac{\pi}{3}(x + 2)\right]$