State the period, amplitude, max/min values, range, domain, horizontal phase shift and vertical displacement .
y=-2sin[ 360 (t+1)/3)]
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range = [-2,2]
the (-2) tells us the amplitude; which means it fluctuates between 2 and -2. This is also the range since it cannot go outside of [-2,2]
becuase the 2 is negative to begin with we know that the graph is flipped over from a normal sine graph; ie, goes down before it goes up.
there is nothing added to the end of the equation to shift the y from its normal position so no vertical displacment.
we can simply the innards by making (360/3) reduce to 120. which gives us the frequency; or how many cycles it has in 2pi. In this case, you want to fit 120 cycles into 2pi.
since the (t) has been modified by a (+1) we have a horizontal shift. And the (+1) says that in order to (t) to get back to "0" we need to move it (+1). It makes sense in my head. So the horizontal shift is (-1).
The sin graph normally has no restriction to its domain so neither does this; the domain is still (-inf,inf)
Max and min values would be 2 and -2 respectively. :)