Trigonometric Equations Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

 Basic Trigonometric Equations:

When asked to solve 2x - 1 = 0, we can easily get 2x = 1 and x = 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 2sinx = 1 sinx =

But, we are only half way to the answer!!!

If we recall the graph of , we will remember that there are actually TWO values of for which the = 1/2.

These values are at:

or at 30º and  150º.

If we look at the extended graph of , we see that there are many other solutions to this equation = 1/2.

We could arrive at these "other" solutions by adding a multiple of to .

.

Most equations, however, limit the answers to trigonometric equations to the domain (Always read the question carefully to determine the given domain.)

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:

 Solution:   First, solve for sin x.                            Now, sine is negative in Quadrant III and Quadrant IV.  Also, a sine value of is a reference angle of 45º.   So, consider the reference angle of 45º in quadrants III and IV.

Example 2:

 Solution:   First, solve for tan x.                            Now, tangent is negative in Quadrant II and Quadrant IV.  Also, a tangent value of is a reference angle of 60 degrees.   So, consider the reference angle of 60º in quadrants II and IV.

 How to use your TI-83+/84+ graphing calculator  to solve trigonometric equations. Click calculator.

 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center Created by Frederick Roberts