In this lesson, Professor Perez teaches about substitutions for rational functions of sine and cosine, using Carl Weierstrass's method. Using double angle formulas, reference triangles, and inverse trig functions, he shows how to replace sine x, cosine x, and dx with expressions in terms of u, where u equals tangent of x over 2. With this substitution, he demonstrates how to simplify an integral and solve for the denominator of a quadratic expression, potentially leading to either trig substitution or partial fraction decomposition.
Rational functions with sine and cosines: Karl Weierstrass method.
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