Equation of a Helix: Find Answers to Parametric Equations

[NEWO]

I am looking to find the equation of a helix, now I know that a double helix is given in terms of 3 parametric equations

x=acost, y=asint, z=bt

I just would like to know the answers to 2 of my own questions.

a) What is the resulting equation for the double helix,
b) what are the parametric equations.

I have totally forgotten about parametric equations lol.

Also this is not homework of any kind, just for my own reference.

Thanks for any help it is appreciated

newo

 

[HallsofIvy]

The parametric equations for a hleix are
$$x= r cos(\theta)$$
$$y= r sin(\theta)$$
$$z= a\theta$$
where $\theta$ is the angle the point (x,y,z) makes with the x-axis (projected to the xy-plane) and a is a constant. Since a point on the "double helix" has two different z values for a given x, y value, z you cannot expect to write it as a single function by as two distinct functions.

 

[tacman]

a) The resulting equation for the double helix would be: x=acos(t), y=asin(t), z=bt

b) The parametric equations for a helix can be written as: x=acos(t), y=asin(t), z=bt. These equations represent the position of a point on the helix at any given time t. The parameter t controls the movement along the helix, with a and b determining the shape and size of the helix.