Hi everyone ! It's Ella.

I'll be summarizing what we have learnt today. The topic was translation of sine and cosine functions. To start it off, let me recall about what Mr. Piatek discussed last week.

Transformations of some and cosine functions
The formulas are:
y = asinbx and y = acosbx

In vertical stretches :
• amplitude changes from the basic of 1 to |a|.

Amplitude is equal to maximum - minimum divided by 2.

•if a < 0, the function is reflected through the horizontal middle axis of function.

In horizontal starches:

• period changes from the basic of  2p to 

•if b < equal to 0, the function is reflected in the y - axis.

Now going to translation of sine and cosine functions.

y = asinb(x-c)+d and y = acosb(x-c)+d

Horizontal translations

•if it's negative, the function shifts c units to the right. 

•if it's positive, the function shifts c units to the left.

•it's called the phase shift.

vertical translations

• called vertical displacement. It is the result of change in the middle axis.

•if it's positive, the function shifts d units up.

•if it's negative, the function shifts d units down.

Order for applying transformations:

•perform all horizontal stretches and reflections.

•perform all vertical stretches and reflections.

•perform all translations.

Here's an example:

Now going to graphing the tangent functions

The graph of the tangent function, y = tanx, is periodic, but it is not sinusoidal. Periodic, meaning that it will repeat itself over regular intervals (cycles) of it's domain. Not sinusoidal, meaning that it does not fluctuate back and forth like a sine or cosine graph. 

Here's an example of tangent graph :