Thursday, 6 October 2011

Sinusoidal Functions of the form f(x) = a sin/cos [k (x-d)] + c

SINUSOIDALLLLLL! (big bombastic word here) ; but it is not self-explanatory. the things under it is not as bombastic as it sounds. hehehehehe...

As usual, when you get a function  f(x) = a sin/cos [k (x-d)] + c,

|a| = amplitude of the graph (refer to the previous 2 posts for a clear definition of an amplitude)
k = horizontal stretch / compression
d = horizontal shift
c = vertical shift

The only thing that's gonna be new here is the method to find the graph's period, given its equation. Using the formula
2π / k = Period
remember, k is the horizontal stretch / compression you can determine by the equation given. Hence, substitute k into the formula, and you will be able to find the period of your trigonometric graph.

Example,
Transform a sine function such that g(x) has amplitude 4, period π, phase shift π/6rad and 2 units up.

Using the formula given above,
the period of the function = 2π/k = π. Therefore, k is 2.
Hence, g(x) = 4 sin [2 (x + π/6)] + 2

I found this exercise quite beneficial especially if ur new to these. After mastering a few questions, you're set and ready to go! (of course, only for this subtopic...hehehe) EXERCISES!

Sayonara!

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