Identifying the parts of a sine graph equation

For the equation     y = 3 sin ( pi/2 x - pi/4 ) - 3     give:
the amplitude of the graph:
the period of the graph:
the vertical translation of the graph:
the phase shift of the graph
a graph of the equation covering one complete period, showing the exact x- and y- coordinates of the highest and lowest point.

SO this is what I know...
the amplitude is 3 since it's the coefficient, the number before sin
and the verticle translation is -3
the period and phase shift is where I am confused because my textbook tells me that:

The graphs of y = A sin (Bx + C) and y = A cos (Bx + C), where B > 0, will have
Period = 2pi / B              Phase Shift =    -C/B

So would that mean the period in the above equation is 2pi / pi/2 = 4?
And the phase shift is -pi/4 / pi/2 = -1/2?
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Here's a picture of your graph done on:
3 * sin ( x * pi/2 - pi/4 ) - 3
This should help you check your answers.
The peaks are at 1.5 and 5.5,
and 5.5 - 1.5 = 4

The bottom peak at 3.5, if no phase shift, would be a 4.
Seems like it is shifted to the left by 1/2.


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>> The graphs of y = A sin (Bx + C) ... where B > 0, will have ... Phase Shift =    -C/B
>> y = 3 sin ( pi/2 x - pi/4 ) - 3
        = 3 sin ( pi/2 x + (-pi/4)   ) - 3
B =  pi/2
C = -pi/4
Phase Shift = -C/B = -(   -pi/4   )/(   pi/2   ) = (   +pi/4   )/(   pi/2   ) = +1/2

The two - signs becomes a + sign, so your answer of -1/2 is off by the sign. Should be +1/2.

Now about the graph. The sin of 0 is 0. Since the sin is translated down by 3, we look for where the sin is -3. It is at ( +1/2, -3 ).

Without a phase shift, you would expect the "start" of the sin wave to be at (0,-3). The sin has been shifted to the right (not the left) by 1/2.

The thing about learning math is that there is no answer you need to trust from anyone. Given hints and statements, you must verify the individual steps yourself. If someone says something that you do not completely agree with or understand, then you should ask about what is concerning you.
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