# Graphs Of Trigonometric Functions :confused: .

• Apr 28th 2006, 01:59 AM
cheesepie
1)At a certain point in the ocean , the veritcal displacement of the water due to wave action is given by y= 3sin[pi/6(t-5)],where y is measured in meters and t is in seconds.
(a)Determine the amplitude ,period, and phase shift for the graph of this wave action.
(b)Sketch one complete cycle of this function.

2)In an ac circuit with only a constant inductance, the voltage is given by
v=12sin(120pi(t)+0.5pi)
a)Determine the amplitude ,period, and vertical displacement of this function
b)Sketch the graph of this function for one period.Make sure that you label the times on the x-axis where the graph crosses the axis and where it is at its highest and lowest points
• Apr 29th 2006, 08:27 AM
CaptainBlack
Quote:

Originally Posted by cheesepie
1)At a certain point in the ocean , the veritcal displacement of the water due to wave action is given by y= 3sin[pi/6(t-5)],where y is measured in meters and t is in seconds.
(a)Determine the amplitude ,period, and phase shift for the graph of this wave action.
(b)Sketch one complete cycle of this function.

For a "signal" $y(t)=A\sin( \omega t + \phi)$, the amplitude is
$A$, the period is $2 \pi/ \omega$, and the initial phase is $\phi$.

In this case we have:

$
y(t)= 3 \sin[\frac{\pi}{6}(t-5)]=3 \sin[\frac{\pi}{6} t -\frac{5\pi}{6}]
$
,

so the amplitude is $3$, the period is $(2 \pi)/(\pi/6)=12$,
and the initial phase is $-5 \pi/6$.

RonL
• Apr 30th 2006, 01:25 AM
CaptainBlack
Quote:

Originally Posted by cheesepie

2)In an ac circuit with only a constant inductance, the voltage is given by
v=12sin(120pi(t)+0.5pi)
a)Determine the amplitude ,period, and vertical displacement of this function
b)Sketch the graph of this function for one period.Make sure that you label the times on the x-axis where the graph crosses the axis and where it is at its highest and lowest points

There is no vertical displacement (it would be an additive constant outside
the sin.

Otherwise this is similar to the previous problem

RonL
• May 5th 2006, 02:13 AM
cheesepie
any step ?

2)In an ac circuit with only a constant inductance, the voltage is given by
v=12sin(120pi(t)+0.5pi)
a)Determine the amplitude ,period, and vertical displacement of this function
b)Sketch the graph of this function for one period.Make sure that you label the times on the x-axis where the graph crosses the axis and where it is at its highest and lowest points
• May 7th 2006, 06:18 PM
Jameson
Please refrain from "bumping" posts. I understand on other forums this is quite common, but there is no need here. All of the moderators and others who help out will look for new posts. Thank you.