Parametric Equations
Exercises for students
Solve the following on paper and check your answers using the above applet:
The coordinates (x, y) of a point on a curve are given in terms of a parameter t by x = 1 + t^2 , y = t^3 - t .
Find the equation of the tangent at the point where t = 1.
Find the equation of the normal at the point where t = 1.
The coordinates (x, y) of a point on a curve are given in terms of a parameter t by x = 2t , y = 1/t^2 .
Find the equation of the tangent at the point where t = 2.
Find the equation of the normal at the point where t = 2.
The coordinates (x, y) of a point on a curve are given in terms of a parameter t by x = cos(2t) , y = sin(3t) .
Find the equation of the tangent at the point where t = 3.14.
Find the equation of the normal at the point where t = 3.14.
The coordinates (x, y) of a point on a curve are given in terms of a parameter t by x = cos(t) , y = sin(2t) .
Find the equation of the tangent at the point where t = 1.57 = pi/2.
Find the equation of the normal at the point where t = 1.57 = pi/2.
The coordinates (x, y) of a point on a curve are given in terms of a parameter t by x = sin(2t) , y = t^2 - t .
Find the equation of the tangent at the point where t = 0.
Find the equation of the normal at the point where t = 0.
The coordinates (x, y) of a point on a curve are given in terms of a parameter t by x = sin(2t) , y = t^3 - t .
Find the equation of the tangent at the point where t = 0.
Find the equation of the normal at the point where t = 0.
You can define the function using the following operators:
| + | - | * | / | ^ |
| sqrt( ) | ln( ) | exp( ) | pi |
| sin( ) | cos( ) | tan( ) |
| asin( ) | acos( ) | atan( ) |
| sinh( ) | cosh( ) | tanh( ) |
Right-click here to download this page, the Java Class File and unzip the Javathings Math Package.
This applet uses the com.javathings.math package developed by:
Patrik Lundin
patrik@javathings.com
http://www.javathings.com