That's a good start. Now just set -cot(t) = 1/2 and solve for t.reconrusty said:Homework Statement
Find all the points on the following curves that have the given slope:
x=4cost
y=4sint
slope=1/2
Homework Equations
The Attempt at a Solution
Im not to sure what to do with this question.. I found dy/dx to be -cot(t) but I am not sure if that is even needed for this problem. Any help would be greatly appreciated !
Parametric equations are a set of equations that describe the x and y coordinates of a point in terms of a third variable, usually denoted as t. This allows for a more flexible representation of a curve or surface compared to traditional rectangular equations.
To graph parametric equations, you can plot several points by substituting different values of t into the equations. Then, connect the points to create a smooth curve or surface. You can also use a graphing calculator or software to graph parametric equations.
The slope of a parametric curve at a given point is determined by the derivative of the x and y equations with respect to t, commonly denoted as dx/dt and dy/dt. These derivatives represent the rates of change of x and y with respect to t, which can be interpreted as the slope of the tangent line at that point.
To find the slope of a parametric curve at a given point, you can use the derivatives of the x and y equations with respect to t. Simply plug in the value of t for the point you want to find the slope at, and evaluate the derivatives to calculate the slope. Alternatively, you can use the slope formula (y2-y1)/(x2-x1) with the coordinates of two points on the curve.
Parametric equations are used in various fields such as engineering, physics, and computer graphics to model and analyze curves and surfaces. For example, they can be used to represent the path of a projectile, the motion of a pendulum, or the shape of a roller coaster track. They are also used in computer graphics to create realistic 3D images and animations.