Maxima Tutorial 3 – Trigonometric Functions and Calculus

In this tutorial, we are going to discuss some of the most elementary commands used in Maxima in Trigonometry and Calculus. Note that in maxima, most constants are written with the percent sign before it. For instance, the most common constants are π, e and i are written as %pi, %e and %i.

Maxima can perform the following trigonometric and calculus operations:

  • Get the value of trigonometric functions
  1. sin(%pi/2);
  2. cos(%pi/4);
  3. tan(%pi/6);
  4. [sin(%pi/3),cos(%pi/3)];

As you can see, in 4, we can get the values simultaneously by separating the functions with comma and enclosing them with bracket.

  • Get the Limits of Functions
  1. computes the limit of 2x3 + 5x2– 2x as x approaches -1: limit(2*x^3 + 5*x^2 – 2*x – 1, x, -1);
  2. computes the limit of (x4 + 4x2)/(2x4 – 2) as x approaches negative infinity: limit((x^4 + 4*x^2)/(2*x^4 – 2), x, minf);
  3. computes the limit of (x4 + 4x2)/(2x4 – 2) as x approaches infinity: limit((x^4 + 4*x^2)/(2*x^4 – 2), x, inf);
  • Get the Derivatives and Integrals of Functions
  1. Get the derivative of derivative of (x4 + 2x3 + 5x2): diff(x^4 + 2*x^3 + 5*x^2, x);
  2. Perform indefinite integration: integrate(x^3 + 4*x^2 – 2*x, x);
  3. Perform definite integration: integrate(x^3 – 2*x^2 + x, x, -1, 2)