# Thread: graphing transformations of trig functions

1. ## graphing transformations of trig functions

y = 0.5sin(x/4 - x/16) -5

I might be dooing it wrong but i rearanged it to
y = 0.5sin(x - x/4) -5

is this correct?
in any case, what would be the period and x translation?

2. Originally Posted by Plzhelp
y = 0.5sin(x/4 - x/16) -5
$\displaystyle \frac{x}{4}- \frac{x}{16} = \frac{4x}{16}- \frac{x}{16} = \frac{3x}{16}$

3. Originally Posted by Plzhelp
y = 0.5sin(x/4 - x/16) -5

I might be dooing it wrong but i rearanged it to
y = 0.5sin(x - x/4) -5

is this correct?
in any case, what would be the period and x translation?
are you sure you didn't mean this equation ...

$\displaystyle \displaystyle y = 0.5\sin\left(\frac{x}{4} - \frac{\pi}{16}\right) - 5$

???

4. Originally Posted by Plzhelp
y = 0.5sin(x/4 - x/16) -5

I might be dooing it wrong but i rearanged it to
y = 0.5sin(x - x/4) -5

is this correct?
in any case, what would be the period and x translation?
$\displaystyle y = A\sin(Bx+C) + D$

A is the amplitude - this is how "high" the graph will go relative to$\displaystyle \pm 1$. For example if A = 2 the extrema will be $\displaystyle \pm 2$

B affects the period of the graph. For $\displaystyle B>1$ the graph will have a shorter period and for $\displaystyle B<1$ a longer period. On a graph this means that the wave will be more or less "squashed" on the x axis respectively.

C is the phase difference which determines the shift on the x axis of the graph. The shape doesn't change, just it's positions and intercepts. For $\displaystyle C>0$ the graph will move to the left and for $\displaystyle C<0$ to the right. $\displaystyle C=0$ is no change obviously enough

D is the y-shift. In other words how much the whole graph is shifted either up or down the y axis.

In your case you have

• $\displaystyle A = 0.5$
• $\displaystyle B = 13/16$
• $\displaystyle C = 0$
• $\displaystyle D = -5$

I have plotted the graphs of $\displaystyle y = 0.5\sin(13x/16)$ in orange, $\displaystyle y = \sin(13x/16)$ in green and $\displaystyle y = \sin(x)$ in blue for comparison purposes

$\displaystyle y = 0.5\sin(13x/16) - 5$ is on a separate attachment

5. @ skeeter, yes thats what i meant to write.

ok thanks for the help e^, I get all of this I just don't know how to get the B from (x/4 - pi/16)

nvm this is easy, thx for the fast response!