SA/Amplitude/Period <-> Equation (now with HW!)

Our final topic in this chapter has been using the period, sinudoidal axis, and amplitude to find the equation of a sinusoidal function.

The homework questions were copied down in class, but I will put a photograph of them here on Saturday.

(Refresher)

The sinusoidal axis:

• y = (vertical translation), or
• y = 0 (if there is no VT)

The amplitude

• equal to the vertical stretch
• equal to 1 (if there is no VS)

The period

• equal to 360 * (horizontal stretch)
• equal to 360 (if there is no HS)

Keep in mind going from the transformations to the equation requires you to take the reciprocal (if there is a stretch) or additive inverse (ie change the sign, if there is a translation)

eg. For a graph of the function y=sinx with a HS of 1/3 and a VT of 4, the equation is:

y - 4 = sin[3x]

HW from front board: Find the (a) transformations and (b) the equation of the graph of y=sinx which has ...

i) Period of 180, sinusoidal axis of y=2, and Amplitude of 4
ii) Period of 120, Maximum of 6, minimum of -2
iii) Period of 90, Maximum of 2, Minimum of 6