Question

Sketch the graph, showing one complete cycle. State the period and amplitude, and the greatest and least values of yy=3sin(θ−π/2)

Answer 1

Explanation:

Consider the following general periodic function:

$y=a\sin b(\theta\text{ -h})\text{ +k}$

where

a= amplitude

b = frecuency

h= phase translation

k= vertical translation

2π/ |b| = period

Now, consider the following periodic function:

$y=3sin(\theta\text{ -}\frac{\pi}{2})$

Applying the definition given at the beginning of this explanation, we can see that:

a = amplitude = 3

2π/ |b| = period = 2π/|1| = 2π

Then, the graph of the given function is:

Notice that the greatest and least values of y are 3 and -3 respectively.

We can conclude that the correct answer is:

Answer:

Graph:

Period:

$2π$

Amplitude:

$3$

The greatest value of y (coordinate y of the maximum point):

$3$

The least value of y (coordinate y of the minimum point):

$\text{ -3}$