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cmut
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I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d2y/dx2=(-3cosec3θ)/49
You could post what you tried so far.I have tirelessly tried to solve this
dx/dθ= -7 sin(θ) and dy/dθ= 3 cos(θ) so dy/dx= (-3/7) cot(θ)cmut said:I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d2y/dx2=(-3cosec3θ)/49
Parametric equations are a set of equations that express a set of coordinates (x, y) in terms of one or more parameters, typically denoted by t. This allows for a more versatile way of representing curves and allows for the manipulation of the curve by changing the parameters.
Parametric equations are used to represent curves that cannot be expressed in the form of a function, such as circles, ellipses, and spirals. They also allow for more control and manipulation of the curve by changing the parameters, making them useful in many applications in physics, engineering, and science.
To solve parametric equations, you can use the same techniques as you would for solving regular equations. The first step is to eliminate the parameter (usually t) by solving for it in one equation and substituting it into the other equation. This will give you an equation in terms of x and y, which you can then solve using algebraic techniques.
One common mistake is forgetting to eliminate the parameter and trying to solve for x and y independently. Another mistake is not properly simplifying the equations before solving, which can lead to incorrect solutions. It's also important to pay attention to the domain of the parameter and make sure to account for any restrictions when solving the equations.
You can check your solution by graphing the parametric equations and seeing if the points you obtained from solving the equations lie on the graph. You can also substitute the values of x and y back into the original parametric equations to see if they satisfy them. It's always a good idea to double-check your work to ensure accuracy.