SOLUTION: Find the amplitude, Period, Phase Shift, Graph and max/min and x and y intercepts of:
g(t) = -2sin(πt + π/3)
Please give a detailed answer for this. I think I under
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-> SOLUTION: Find the amplitude, Period, Phase Shift, Graph and max/min and x and y intercepts of:
g(t) = -2sin(πt + π/3)
Please give a detailed answer for this. I think I under
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Question 920439: Find the amplitude, Period, Phase Shift, Graph and max/min and x and y intercepts of:
g(t) = -2sin(πt + π/3)
Please give a detailed answer for this. I think I understand the amplitude being the height from the negative or positive of the y axis. And therefore it would be from 2 to -2? And it's always the absolute of the first number.
The period I think is the number of times It goes around and I think that is the π/3 part
The phase shift not sure
and how to find the max and min, not sure
or the x and y intercepts.
Please help
Thank you Answer by Theo(13342) (Show Source):
|a| is the amplitude
b is the frequency
c is the horizontal shift
d is the vertical shift.
replace t with x and your equation is:
y = -2 * sin( pi * x + pi/3)
this can also be written as:
y = -2 * sin( pi * (x + 1/3))
the general equation is, once again:
y = a * (sin( b * (x-c)) + d
in your equation:
|a| = 2
b = pi
c = 1/3
d = 0
your amplitude is equal to 2
your frequency is equal to pi
your horizontal shift is equal to -1/3
your vertical shift is equal to 0
your period is equal to 2*pi divided by your frequency.
this makes your period equal to 2*pi / pi = 2
everything is in radians.
your equation looks like this:
the period is equal to 2 and goes from -1/3 to 5/3.
your amplitude is equal to 2 so the graph goes from a high of 2 to a low of -2.
there is no vertical shift because d = 0.
take away the horizontal shift and your graph looks like this:
everything else remains the same except there is no more horizontal shift so the period goes from 0 to 2.
your y intercept is the value of y when x = 0.
your equation is, once again:
y = -2 * sin( pi * (x + 1/3))
when x = 0, y = -2 * sin(pi/3)
pi/3 = 60 degrees and sin (60) = sqrt(3)/2
-2*sqrt(3)/2) = -sqrt(3) which is equivalent to -1.73.....
you can see that on the following graph.
that's the value of y when x = 0
the x-intercept is the value of x when y = 0
set your equation and solve for x.
you get:
0 = -2sin(pi(x+1/3))
divide both sides by -2 and you get:
sin(pi(x+1/3) = 0
this is true if and only if arc-sine(0) = pi(x+1/3)
arc-sin(0) = 0 so pi(x+1/3) = 0 which results in x = -1/3.
the value of y is 0 when x = -1/3.
here's a good reference on the general formula used.
