Another Tough Lesson!!!
Melfi – Forgot to talk about
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
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
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: sin x 2 sin x
Solve for x from 0 to 2: 2 tan x 2 3 0
Solving Quadratic Equations