Question

-Is this a sine function or cosine? How do you know?

-Whats the amplitude?
-What’s the time period ? What’s the value of B?
-What’s the equation of the midline?
-Determine an equation for this graph

Answer 1

a) Cosine function

b) amplitude=1

c) Period=π, b=2

d) y=0

e)

`y = - \cos(2x)`

Explanation:

a)Since the graph is symmetric with respect to the y-axis, it is a cosine function. This time the cosine function is reflected in the x-axis.

b) The graph ranges between -1 and 1, therefore we have the amplitude to be |-1|=|1|=1

c) The graph completes one full cycle within every π units. Therefore the time period is π. Also the value of b is 2, because the graph repeats twice on the interval [0,2π]

d) The midline divides the graph into two equal halves.

The midline has equation y=0.

e) The equation of this graph is of the for m,

`y = - a \cos(bx)`

where a=1 is the amplitude and b=2 is the frequency.

Therefore the equation is :

`y = - \cos(2x)`