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
A parametric equation is a set of equations that express a set of variables, typically denoted as x and y, as functions of an independent variable, typically denoted as t. It is commonly used to represent curves and surfaces in mathematics and physics.
To convert a parametric equation to cartesian form, the independent variable t is eliminated by solving for it in one of the equations and substituting the result into the other equation. This will result in an equation in terms of x and y, which is the cartesian form.
Parametric equations allow for a more efficient and versatile way of representing curves and surfaces, especially ones that are not easily expressed in cartesian form. They also provide a way to represent motion and changes over time, making them useful in physics and engineering.
Yes, any curve can be represented by a parametric equation. However, some curves may be more easily expressed in cartesian form, while others may require more complex parametric equations to accurately represent them.
Parametric equations are used in a variety of real-world applications, including computer graphics, engineering, and physics. They are particularly useful for representing motion, such as the trajectory of a projectile, and for creating 3D models of objects and surfaces.