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I am sorry m8 Can't help
im only in Algebra 2
Not sure which one you need help with.
part a) just look for graph that matches y=5 sin(x+pi) let's try to draw a graph here. the amp=5 the period=2pi the phase shift is -pi can you graph y=5sin(x+pi)?
1st questions answer looks like option A
@freckles so the answer to prt a of the question is answer choice "A"
yes that looks good you can also plug in numbers like 0 and -pi/2 and -pi and so on to help you pick out the right one
what are the x-intercepts of y=5sin(x+pi) in that graph
so part a is "A"
I dont know what the x intercepts are
do you know hot solve sin(x+pi)=0?
that will give you the x-intercepts if it isn't clear from the graph A
so that is answer choice C
|dw:1438062133167:dw| hmmm... you should know that sin(2pi+pi)=0 and sin(pi+pi)=0 and sin(0+pi)=0 and sin(-pi+pi)=0 and sin(-2pi+pi)=0 and sin(-3pi+pi)=0
|dw:1438062355237:dw| this is what the graph should look like if it is not clear where the max values are 5 and the min values are -5
the x-intercepts is where the graph touches the x-axis
Oh so the answer choice is B
let's look at graphing y=5csc(x+pi) not recall csc and sin are reciprocals of each other so sin(x+pi) will be reciprocal value of csc(x+pi) for x if sin is 0 then csc is what?
the only number that doesn't have a reciprocal is 0 right?
so when sin is 0 you have a vertical asymptote for csc
but say sin is 1 then csc is ?
remember sin and csc are reciprocal functions
just flip the number
right and 5(1)=5 so both sin and csc will share the following common points |dw:1438062820709:dw|
we also know if sin is -1 then csc is -1 so we know that the graph will also share |dw:1438062857511:dw|
now just draw the little U things in between the broken lines so that it is getting closer and not touching
ok so those are the relative maximum and minimum points
the maxes of the sin function are the relative mins of the csc function the mins of the sin function are the relative maxs of the csc function
so what are the coordinates of the relative maximum and minimums of the csc function, im sorry im not tryng to get all the answers out of you because there is another problem just like this and I would like to finish this one fast to see if I can do the next one!
so a relative min/max occurs when the graph is turning but the difference is on that turn if the turn point is above all other points on the subinterval then it is a relative max but if the turn point is below all other points on the subinterval then it is a relative min for example |dw:1438063333098:dw|
the graph I recently drawed you shows the relative min and max of y=5csc(x+pi)
it is the curve that is black the green one was the sin function (well the asymptotes are also in green but oh well)
the y coordinates should be clear
the x-coordinate occur midpoint of the zeros
ok, one sec
i think I know the x coordinate for the relative max and min, but i don't know the y coordinate
the y's are the easiest though :p
|dw:1438063703129:dw| so this graph didn't make any sense?
like you see the y=5 line that is where the relative mins of y=5csc(x+pi) occur and the y=-5 line that is where the relative maxs of y=5csc(x+pi) occur
any point laying on the y=5 line has y-coordinate 5 any point laying on the y=-5 line has y-coordinate -5
i see, ok so let me tell you the relative mins and max's
(-5pi/2,5) and (-pi/2,5) are the minnimums
|dw:1438063960901:dw| nice those points are lowest on those little intervals there
(-3pi/2,-5) and (pi/2,-5) are the maximums
|dw:1438063992827:dw| right those points are highest on those little interval there
ok got it!
anyways part e was done I don't even know why they asked you to do c and d before e
so part e is the same graph as part a
oh no, the answer choice for question e is answer choice "b"
but they did include the sin graph to draw the csc graph the sin graph is in broken blue the csc graph is in solid black and yes that is what it looks like on my end for the top part but I think the bottom part of my thing was cut off but C and A definitely don't work for what is shown on them
|dw:1438064471600:dw| that looks like what I have drawn