1. ## Trig transformations

Im having some trouble sketching trig graphs with translations in the direction of the y-axis.

Here is an example from my textbook..

y = 2 sin3x + 1

Is there a good step-by-step method in working these types of questions out? Especially when it comes to working out the x-ints after a vertical translation of 1 unit?

That would be greatly appreciated.

2. Originally Posted by steph_r
Im having some trouble sketching trig graphs with translations in the direction of the y-axis.

Here is an example from my textbook..

y = 2 sin3x + 1

Is there a good step-by-step method in working these types of questions out? Especially when it comes to working out the x-ints after a vertical translation of 1 unit?

That would be greatly appreciated.
$\displaystyle y = a \sin(bx+c) + d$

a changes the amplitude of the wave by a factor of a. (for example $\displaystyle 2 \sin(x)$ is the same as $\displaystyle \sin(x)$ except the peak and minimum values are 2 and -2, not 1 and -1.)

b changes the frequency of the sine wave by a factor of b. ( for example $\displaystyle \sin(2x)$ has twice the frequency of $\displaystyle \sin(x)$. So it only takes $\displaystyle \pi$ radians (or 180 degrees) for a full wave, instead of $\displaystyle 2\pi$ (or 360 degrees)).

c translates the graph along the x axis to the left by c places.

d translates the graph along the y axis upwards by d places.