Tangents & Normals
Exercises for students
Solve the following on paper and check your answers using the above applet:
Find the equation of the tangent at the point (0, 0) on the curve y = sin(x).
Find the equation of the normal at the point (0, 0) on the curve y = sin(x).
Find the equation of the tangent at the point (1, 1) on the curve y = x^2.
Find the equation of the normal at the point (1, 1) on the curve y = x^2.
Find the equation of the tangent at the point (1, 2) on the curve y = sqrt(x^2 + 3).
Summary
The tangent to a curve at the point ( x0 , y0 ) is given by:
| y - y0 | = m0 |
| __________ |
| x - x0 |
The normal to a curve at the point ( x0 , y0 ) is given by:
| y - y0 | = | - 1 |
| __________ | ___ |
| x - x0 | m0 |
where m0 is the gradient to the curve at ( x0 , y0 ).
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