Solve (6cost t, 6sint, 6cos2t) = (3√3, 3, 3) for t .Jimerd said:Homework Statement
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = 6 cos t, y = 6 sin t, z = 6 cos 2t; (3√3, 3, 3)
Homework Equations
The Attempt at a Solution
So I understand that r(t)= 6cost t, 6sint, 6cos2t
and r'(t)= -6sint, 6cost, -12sin2t
So here is the questions, how do I find what the value of t is at points (3√3, 3, 3)
A parametric equation is a way of expressing a set of equations with multiple variables in terms of a single parameter. This allows for a more efficient and organized way of representing complex relationships between variables.
To find t in a parametric equation, you can use the method of substitution. This means that you substitute the given values for the other variables in the equation, leaving t as the only unknown variable. You can then solve for t using algebraic methods.
Parametric equations are useful because they allow for a simplified representation of complex relationships between variables. They are also commonly used in physics and engineering to model motion and other dynamic systems.
Yes, a parametric equation can have multiple parameters. This means that the equation will have multiple unknown variables that can be solved for using different methods. However, it is important to note that adding more parameters can also make the equation more complicated and difficult to solve.
Parametric equations have many real-world applications, including in physics, engineering, and computer graphics. They are commonly used to model the motion of objects, such as projectiles or vehicles, and to create visual effects in movies and video games.