Trigonometric Equations

 Basic trigonometric equations in sine, cosine, and tangent. They can be introduced any time after the unit circle definitions. These equations are either quadratic in sine, cosine, or tangent, or can be factored. Once we factored, we have to solve basic trigonometric equations as in Trigonometric Equations 1. These equations can be introduced after the compound angle identities. Usually, after the application of a double-angle formula, the equation becomes like one on the previous set, Trigonometric Equations 2. (Where the fun begins.) These equations are basic trigonometric equations but not in x, but rather in 3x, 4x, 5x, etc. This handout explores what it means to divide on the unit circle. Turns out we multiply the points on the unit circle when we do that. There is a method to transform any linear combination of sine and cosine (for example 2sinx-5cosx) into a single trigonometric expression. This is not just a very interesting method, but has applications to graphing trigonometric functions, to optimization of trigonometric functions, and is often a method that enables solving trigonometric equations. Trigonometric Equations 6to be posted To solve equations of the form sinA=sinB or SinA=cosB. Until now, only one side of the equation was a trigonometric expression. Trigonometric Equations 7to be posted A comprehensive collection of mixed trigonometric equations in which techniques from more than one previous problem set come up. In short, fun.