Addition of Ordinates of Sine and Cosine

[Karapl13]

Hello

I am currently stuck on this quesiton

y= 2cos2(x) + 3sin(2x) where the domain is between negative pie and positive pie and it needs me to sketch the graph

I have tried but I am still stuck on this question, any help would be appreciated

Thank you

[mohfame]

hey, im not sure but i think it's a specialist question.
because i tried to do the question but i wasn't able to get all the coordinates perfectly.
 maybe post it on the specialist thread...

[Sine]

Hello

I am currently stuck on this quesiton

y= 2cos2(x) + 3sin(2x) where the domain is between negative pie and positive pie and it needs me to sketch the graph

I have tried but I am still stuck on this question, any help would be appreciated

Thank you

Hey !

This question is definitely inside the scope of the methods course however only extremely rarely crops up (last time it came up was like 1997  )
Addition of ordinates is so annoying an tedious but these tips should hopefully help
Graph both graphs on the one set of axis i.e. 2os(2x) and 3sin(2x).
Since the graph we want to graph is the sum of these two "all" we need to do is take each x-value - find both y-values and add them together. Simple? not really gets pretty messy.
To make it easier for you find the x-intercepts of each graph and the y-value of our required graph will be at the EXACT same y-value as the other graph (the one which doesn't have the x-intercept at that point).
Also when each graph has the negative value of the other graph i.e. y=2.524 and y=-2.524 we can conclude that the graph we required will have a x-intercept at that point. (y=0).
Other points can be found by adding the y-value of both graphs i.e. y=2 and y=3 , then we can say that the y-value we require for our graph is y=5.

[TooLazy]

hey, im not sure but i think it's a specialist question.
because i tried to do the question but i wasn't able to get all the coordinates perfectly.
 maybe post it on the specialist thread...

mad cuz gads, sine said it was a methods question

[mohfame]

Hey !

This question is definitely inside the scope of the methods course however only extremely rarely crops up (last time it came up was like 1997  )
Addition of ordinates is so annoying an tedious but these tips should hopefully help
Graph both graphs on the one set of axis i.e. 2os(2x) and 3sin(2x).
Since the graph we want to graph is the sum of these two "all" we need to do is take each x-value - find both y-values and add them together. Simple? not really gets pretty messy.
To make it easier for you find the x-intercepts of each graph and the y-value of our required graph will be at the EXACT same y-value as the other graph (the one which doesn't have the x-intercept at that point).
Also when each graph has the negative value of the other graph i.e. y=2.524 and y=-2.524 we can conclude that the graph we required will have a x-intercept at that point. (y=0).
Other points can be found by adding the y-value of both graphs i.e. y=2 and y=3 , then we can say that the y-value we require for our graph is y=5.

Hey
Question, won't it be easier to just convert one of them into sine or cosine and do the graph ?

[Syndicate]

Hey
Question, won't it be easier to just convert one of them into sine or cosine and do the graph ?

That's perfectly fine. It would be better to convert cos(2x) to 1-2sin^2(x) than anything else in my opinion.

As for the turning points, you will need to calculate the (x,y) coordinates by either using differentiation or locating the points of intersection between the two functions (which can be done by equating 2cos(2x) to 2sin(2x) ).