why do we use parametric equations in calculus?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

why do we use parametric equations in calculus?

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

one simple answer is that sometimes it's impossible to describe a curve in the form of y=f(x) since it fails the vertical line test.. the x- and y- coordinates can be each described separately as a function of a parameter "t" for example
I hope that made sense to you
sometimes parametric equations are homogeneous or symmetric .. elegant,that is... while the y = f(x) form is ugly

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

parametric equation...Think of a curve being traced out over time, sometimes doubling back on itself or crossing itself. Such a curve cannot be described by a function y=f(x). Instead, we will describe our position along the curve at time t by x y = = x(t) y(t) Then x and y are related to each other through their dependence on the parameter t. Example Suppose we trace out a curve according to x y = = t2−4t 3t where t0. The arrow on the curve indicates the direction of increasing time or orientation of the curve. Drag the box along the curve and notice how x and y vary with t. The parameter does not always represent time: Example Consider the parametric equation x y = = 3cos 3sin Here, the parameter represents the polar angle of the position on a circle of radius 3 centered at the origin and oriented counterclockwise. Differentiating Parametric Equations Let x=x(t) and y=y(t). Suppose for the moment that we are able to re-write this as y(t)=f(x(t)). Then dtdy=dxdydtdx by the Chain Rule. Solving for dxdy and assuming dtdx=0, dxdy= dtdx dtdy a formula that holds in general. Example If x=t2−3 and y=t8, then dtdx=2t and dtdy=8t7. So dxdy dx2d2y = = dtdxdtdy=2t8t7=4t6 ddxdxdy= dtdx dtd[dxdy] =2t24t5=12t4 Notes * It is often possible to re-write the parametric equations without the parameter. In the second example, x3=cos, y3=sin. Since cos2+sin2=1, x32+x32=1 . Then x2+y2=9, which is the equation of a circle as expected. When you do eliminate the parameter, always check that you have not introduced extraneous portions of the curve. * Every curve has infinitely many parametrizations, amounting to different scales for the parameter. For example, x y = = 3cos2 3sin2 traces out the circle from the second example twice as "quickly," completing a full revolution in rather than 2 units of . * Every equation y=f(x) may be re-written in parametric form by letting x=t, y=f(t). Key Concepts A curve in the xy-plane may be described by a pair of parametric equations x=x(t) y=y(t) where x and y are related through their dependence on t. This is particularly useful when neither x nor y is a function of the other. The derivative of y with respect to x (in terms of the parameter t) is given by dxdy=dtdxdtdy
great ans!!!!
thanks saurabh..

Not the answer you are looking for?

Search for more explanations.

Ask your own question