Question

State the period, amplitude, max/min values, range, domain, horizontal phase shift and vertical displacement .

y=-2sin[ 360 (t+1)/3)]

Answer 1

period:2pi/3
amplitude:-2
max:2 (-1<=sinx<=1)
min:-2
range = [-2,2]

Answer 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)

Answer 3

Max and min values would be 2 and -2 respectively. :)

Answer 4

period is wrong .it is pi/60...if you take 360 as a number and "6" if you take 360degree . so just make clear it only 360 or 360degree