Description

This topic explores further applications of Trigonometry such as The Law of Sines (and it's ambiguous case), the Law of Cosines; the Trigonometric Form of complex numbers as well as Demoivre's Theorem to find powers and roots of complex numbers. We finish this topic by exploring vectors, how to sketch vectors in a plane, arithmetic operations of vectors and the dot product between two vectors.

Sections of this topic include:

1. The Law of Sines to Solve Triangles

   Studying how to solve sides and angles of triangles that are not right triangles, we begin with the Law of Sines. Groups in this section include using the Law of Sines to solve triangles; the ambiguous case of the Law of Sines; and finding areas of triangles.

2. The Law of Cosines

   Continuing our study of solving non-right triangles, we investigate the Law of Cosines. Groups within this section include using the Law of Cosines to solve triangles; and applications of the Law of Cosines.

3. Trigonometric Form of Complex Numbers

   An interesting application of Trigonometry is with complex numbers. Groups within this section include finding the absolute value of a complex number; graphing complex numbers; writing complex numbers in trigonometric form; writing complex numbers in rectangular form; finding products and quotients of complex numbers in trigonometric form.

4. De Moivre's Theorem

   A French Mathematician named Abraham de Moivre discovered how to find powers and roots of complex numbers in trigonometric form. To this end, we study his theorem to find these results. Groups within this section include using De Moivres Theorem to find complex numbers to a power; finding roots of complex numbers; solving equations by finding roots of complex numbers.

5. Vectors

   Another useful application of trigonometry is the study of vectors for mathematics and physics. This section introduces the concepts of Vectors for later study. Groups within this section inlcludes performing vector arithmetic; sketching vectors; proving vector properties; finding magnitudes and angles of vectors.

6. The Dot Product of Two Vectors

   Finishing our study of vectors, we conclude with the notion of the dot product of two vectors. Groups within this section include finding dot products and angles between two vectors; and showing two vectors are orthogonal.