ABSTRACT
The seventh chapter presents a wealth of proofs on trigonometric functions. It starts from the definitions and basic properties and then proves most common trigonometric identities, such as those for the sum and the difference of angles or for the sum and the product of trigonometric functions. Separate sections discuss polar coordinates and the multiplication of complex numbers — topics that are intimately linked with trigonometry. Another section returns to the discussion of the Fundamental Theorem of Algebra. It presents a chain of arguments that illustrates why one should expect this theorem to be true. The chapter concludes with a section on analytical geometry, proving the law of cosines and the law of sines.
