Basic Trigonometric Equations:
When asked to solve 2x - 1 = 0, we can easily get 2x = 1 and x = d 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 = d
But this is only part of the answer.

If we look at the graph of sinθ from 0 to 2π,
we will remember that there are actually
TWO values of θ for which the sinθ = d.

These values are at:

or at 30º and  150º.

If we look at the extended graph of sinθ , we see that there are many other solutions to this equation sinθ = d

We could arrive at these "other" solutions by adding a multiple of 2π to θ.


where n is an integer in [0,∞).


Most equations, however, limit the answers to trigonometric equations to the domain
[0, 2π] or [0º, 360º].  (Always read the question carefully to determine the given domain.)


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.

ex1     g

Solution: First, solve for sin x.

Now, sine is negative in Quadrant III and Quadrant IV. 

Also, a sine value of j is a reference angle of 45º.   So, consider the reference angle of 45º in quadrants III and IV.





ex2     ;

Solution:   First, solve for tan x.

Now, tangent is negative in Quadrant II and Quadrant IV. 

Also, a tangent value of t is a reference angle of 60 degrees.   So, consider the reference angle of 60º in quadrants II and IV.





For help with trigonometric equations on
your calculator,
click here.
MathBits Calculator Pages


NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
and is not considered "fair use" for educators. Please read the "Terms of Use".