# 6-3 6-4 Graphing Sine and Cosine. Periodic function: A function which has a graph that repeats itself identically over and over as it is followed from.

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6-3 6-4 Graphing Sine and Cosine

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’

Examples: 1) Find the period of each graph

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?

examples

7) Graph y=cos(x) for 3π ≤ x ≤5π

Amplitude: half the distance between the minimum and maximum values of the range of a periodic function. (the ‘height’ of the function

8) Find the amplitude of the graph y = 4cos (x) 9) Graph y=4cos(x) and y=cos(x) and then compare.

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

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