Transformation in Trig Functions: f(x) = sin(pix + 1)

[Idealistic]

How can you identify the transformation in the following equation:

f(x) = sin(pix + 1)

This is what I know:
- There is no Verticle Translation or Verticle Stretch
- There is a Horizontal Translation of 1
- There is a Horizontal Stretch of pi

My questons are:
Is the horizontal stretch actually equal to the reciprical of what is given in the equation (i.e. 1/pi)?
Also, if I answer the qestions using degrees or radians what affect will it have on the horizontal translation of one?
Finally, is the calculation of the period 2pi / pi (360 degrees / 180 degrees) Or 2pi * pi (360 degrees * 180 degrees)

 

[skeeter]

Re: Transformation in Trig Functions

\(\displaystyle f(x) = \sin \left[\pi \left(x + \frac{1}{\pi} \right) \right]\)

horizontal translation to the left \(\displaystyle \frac{1}{\pi}\) units.

normal period for the sine function is \(\displaystyle 2\pi\) ... the period of this function is 2 ... so, call it a horizontal "squeeze" (or compression) rather than a "stretch".