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Chapter six
SOLVING TRIGONOMETRIC
EQUATIONS
Introducing the Topic
In this chapter, you and your students will learn how to solve trigonometric
equations graphically. A trigonometric equation is an equation involving a
trigonometric function. Usually, trigonometric equations are solved for the princi-
pal values for each function. These values are - /2
and 0
x
for cosine. The other solutions will then be the integral multiples of
the function's period. Some trigonometric equations will have no solutions.
To solve an equation graphically, you will graph the left side of the equation as
Y1 and the right side as Y2. In the case where the right side of the equation is
zero, you will graph the left side as Y1 and solve for the intercepts. The point(s)
of intersection will be the solutions to the equation.
Calculator Operations
To solve a trigonometric equation graphically, you will turn the calculator on
and press Y=
done in degrees and radians. Let's do the first one in degrees by pressing 2ndF
SET UP , touching B DRG, and double touching 1 Deg. Press 2ndF
exit the menu. To find the solutions of 3sin
X/ /T/n
)
a
Solving Trigonometric Equations/TRIGONOMETRY USING THE SHARP EL-9600
CL to access and clear Y1 of an old expression. Solving can be
b
2
–
4
sin
x
/2 for sine and tangent,
2
x – 4sin x + 1 = 0, press 3
X/ /T/n
+
1
ENTER .
QUIT to
(
sin
23
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