Trigonometric Parametric Equations

hyptrig.html

Exploration

Show that the parametric equations

x=a sec (θ)

y=b  tan (θ)

represent the hyperbola

.

Approach

Demonstrate that the parametric equations satisfy the equation of the hyperbola.

Initialize

To initialize Descarta2D, select the input cell bracket and press SHIFT-Enter.

This initialization assumes that the Descarta2D software has been copied into one of the standard directories for AddOns which are on the Mathematica search path, $Path.

<<Descarta2D`

Solution

Substitute the parametric values into the equation and observe that the equation is satisfied.

Clear[x,y,a,b,t];
x^2/a^2-y^2/b^2-1 /.
   {x->a*Sec[t],y->b*Tan[t]} //Simplify