6-3 6-4 graphing sine and cosine. periodic function: a function which has a graph that repeats...
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Periodic function: A function which has a graph that repeats itself identically over and over as it is followed from left to right. Formally, a function f is periodic if there exists a number p such that f(x + p) = f(x) for all x.
Period: the horizontal distance required to complete a full ‘cycle’
Graph of y =sinx
a) What is the maximum values? When does it occur?
b) What is the minimum value? When does it occur?
c) What is the period?
d) What is the y intercept?
e) What are the x intercepts? How many are there?
Graph of y =cosx
a) What is the maximum values? When does it occur?
b) What is the minimum value? When does it occur?
c) What is the period?
d) What is the y intercept?
e) What are the x intercepts? How many are there?
Amplitude: half the distance between the minimum and maximum values of the range of a periodic function. (the ‘height’ of the function
The amplitude of y=Asin(θ) or y=A cos(θ) is IAI
The period of y= sin kθ or y =cos kθ is
For example, given the equation y= 3 sin6θ,
The amplitude is 3 and the period is or
10)Find the amplitude and period for the function y = -2cos(4θ)
11) Write a sine function with an amplitude of 6.2 and period of 6π