Question

What is the equation of the function shown in blue.

Answer 1

The y=sin(t) line in red seems to be more compressed, when compared to the blue line

Answer 2

and I can see that the period is between -2pie to pie

Answer 3

except I'm not sure how the 1/2 infront of the sin in answer (b) for example would effect the graph?

Answer 4

informal way to remember
when the number is outside it affects the y, the vertical
when inside it affects the x

Answer 5

pick a value for t let's use pi
sin pi = 0 now sin 2pi = 0

Answer 6

Okay what does that tell us

Answer 7

Is the blue line twice the length the red line or half

Answer 8

not exactly sure, I think its half

Answer 9

Wave length I meant

Answer 10

yeah, sorry not too sure on that one

Answer 11

That was all the info I was provided

Answer 12

No it is twice the length
It is either A or B

Answer 13

Sorry it is taking so long to type
Im doing this on my PS4

Answer 14

Im sorry C or D

Answer 15

@beastieman21 that is not correct

Answer 16

Its not???

Answer 17

the basic graph of y= sin(t) is shown in red

You can see some key features:

It passes through (0,0)
It has a peak at -pi/2 and +pi/2
it has zer values at -pi and +pi
The range of values is from -1 to + 1


IF the equation was y= 2sin(t) you can see that this simply DOUBLES the y value at all points.
Therefore the peak values would be -2 and +2
i.e. the amplitude has changed


IF the equation was y= sin (2t) you can see that this means that the peak will be when 2t = +pi/2 or -pi/2
i.e. the period has changed


You can see that in the BLUE graph
It passes through (0,0)
It has a peak at -pi and +pi
It has zero values at +2pi and -2pi
The range of values is from -1 to + 1

So the amplitude hasn't changed (from the simple equation) but the period has

Answer 18

please note that the function in red has a period which is one half of the period of the function in blue

Answer 19

visually, the number of "full waves" (between 0 and \(2\pi\)) determine the magnitude of the coefficient of \(x\) in the sine function. here are two examples: \(y=\sin(x)\) and \(y=\sin(3x)\)