Trigonometric Equations Another Tough Lesson!!!

Melfi – Forgot to talk about Reference Angles Reference Angles: Associated with every angle drawn in standard position (except quadrantal angles) there is another angle called the reference angle. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Reference angles may appear in all four quadrants. Angles in quadrant I are their own reference angles. Remember: The reference angle is measured from the terminal side of the original angle "to" the x-axis (not the y-axis).

Basic Trigonometric Equations: When asked to solve 2x - 1 = 0, we can easily get 2x = 1 and x = ½ as the answer. When asked to solve 2sinx - 1 = 0, we proceed in a similar manner. We first look at sinx as being the variable of the equation and solve as we did in the first example.

2sinx - 1 = 0 If we recall the graph of sin  from 0 to 2 , we will remember that there are actually TWO values of  for which the sin  =½ These values are at: 30º and 150º Most equations, limit the answers to trigonometric equations to the domain from 0 to 2 

Signs and Quadrants: Solutions of trigonometric equations may also be found by examining the sign of the trig value and determining the proper quadrant(s) for that value. Example 1:

Example 2: Solve for x from 0 to 2  :

Solve:

Solving Quadratic Equations and identities:

Homework Worksheet