The discussion revolves around converting parametric equations, specifically X=cos(t) and Y=2sin(2t), into Cartesian form. Participants are exploring various algebraic manipulations and relationships between the variables.
Some participants have shared their attempts and partial results, while others have provided feedback on the correctness of specific manipulations. There is a recognition of the need to eliminate the parameter t, and some participants express uncertainty about the effectiveness of their approaches.
There are indications of confusion regarding the algebraic steps taken, with some participants questioning the validity of their results. Additionally, a new problem involving x=sec(t) and y=tan(t) is introduced, prompting a suggestion to start a new thread for clarity.
So y = 4sin(t)cos(t). What is y/x?Mrencko said:Homework Statement
I have this equation and i need to find the cartesian equation, so i apreciate your help
Homework Equations
X=cost ' y=2sin2t
The Attempt at a Solution
I am usign this [/B]
Sin2t=2costsint
So x+y/2=cost+2costsint
But i don't know what to do after,
I also try to solve that this way
Y/2=sin2t
Y/2=2costsint then sint=y/(4cost)
Y/2=2((x)y/4x)
When i isolate y i get y/y=3x-2
I doubt that will work.Mrencko said:Thanks for the help i juts figure out how to get rid of that parameter 1-cos alll div by 2
With one correction, that works. Where you have y2 = 16x2(1(cost)^2), it should be y2 = 16x2(1 - cos2(t)). Otherwise, what you ended with is the same as I got.Mrencko said:y=4xsint==>y^2=16x^2(1(cost)^2)=y^2=16x^2(1-x^2)
Using ##1 + \tan^2\theta = \sec^2\theta## is the obvious choice. But you should post new questions in new threads if you don't want to have your hand slapped by a moderator.Mrencko said:Thanks that's it Sorry pal i have anoter problem i am doing x=sect y=tant
So what i need to do use the 1+tan^2=sec^2
Or use the sin/cos=tan and 1/cos = sec? I can get the solution
This is a new problem, so please start a new thread.Mrencko said:Thanks that's it Sorry pal i have anoter problem i am doing x=sect y=tant
So what i need to do use the 1+tan^2=sec^2
Or use the sin/cos=tan and 1/cos = sec? I can get the solution