Townsend said:In case you don't remember the parametric equations of a circle are
x=a*cos(t)
y=a*sin(t)
Where a is the radius and as t increase in the positive direction the circle is traced out in a counter-clockwise direction...
With that and the information quasar987 gave you, you should be able to figure out what to do...
Good luck
A vector valued function is a mathematical function that maps a set of input values to a corresponding set of output values in the form of vectors. It is commonly used to describe the position, velocity, and acceleration of a moving object in a particular direction.
A curve is considered counterwise if it follows a counterclockwise direction, which means it moves in the same direction as the hands of a clock. On the other hand, a curve is considered clockwise if it follows a clockwise direction, which means it moves in the opposite direction of the hands of a clock.
Yes, a curve can have both counterwise and clockwise components. This means that the curve changes direction at certain points, and the vector valued function must be able to account for these changes in direction.
To find a vector valued function for a counterwise or clockwise curve, you need to determine the direction of the curve and then use the appropriate parameterization method. For a counterwise curve, you can use the right-hand rule to determine the direction of the curve, and for a clockwise curve, you can use the left-hand rule.
Vector valued functions for curves have many real-life applications, including in physics, engineering, and computer graphics. They are used to describe the motion of objects, such as the trajectory of a projectile or the movement of a car on a curved road. They are also used in computer graphics to create smooth animations and simulations of real-world movements.