hello again..i have another question...

it says sketch the curve
<3cost,t,2sint>
i know the parametric equations are
x=3cost y=t z=2sint

but what do i do to sketch them..plz help me

(x/3)^2 + (z/2)^2 = 1

In the x,z plane, the object always lies along an elliptical cylinder with semimajor axis = 3 and semiminor axis = 2. It advances along the y axis while following a helical path along the elliptical cylinder

3z/2x = tan t

Use the pair of equations to solve for x and y as functions of t. When t = 0, you start out at z = 0, x = 3

To sketch the curve defined by the parametric equations x = 3cost, y = t, and z = 2sint, you can follow these steps:

1. Choose a range for the parameter t. This will determine the length of the curve you want to sketch. For example, you could choose t to range from -π to π, giving you a curve that represents one full period of the trigonometric functions.

2. Plotting points for different values of t:
- Start by choosing a value for t in your chosen range. For example, you could start with t = -π.
- Substitute this value of t into the equations x = 3cost, y = t, and z = 2sint.
- Calculate the corresponding values of x, y, and z.
- Plot the point (x, y, z) on a coordinate system.
- Repeat this process for other values of t, incrementing or decrementing t as desired, and plot the corresponding points. The more points you plot, the smoother and more accurate your sketch will be.

3. Connect the plotted points with a smooth curve. As you've plotted numerous points, you can now connect them in a way that best represents the shape of the curve. Make sure to maintain the continuity and smoothness of the curve.

4. Optionally, you can add arrows or labels to indicate the direction or key points on the curve if needed.

Remember, the parametric equations give you the coordinates (x, y, z) of points on the curve. By plotting these points and connecting them, you can visualize the shape of the curve in three-dimensional space.