Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.4

17.4 Solving Trigonometric Equations

EMBDE

In Grade 10 and 11 wefocused on the solutionof algebraic equations and excluded equationsthat

dealt with trigonometricfunctions (i.e. sin and cos). In this section, the solution of trigonometric

equations will be discussed.

The methods describedin previous Grades alsoapply here. In most cases, trigonometric identities will

be used to simplify equations, before finding thefinal solution. The finalsolution can be found either

graphically or using inverse trigonometric functions.

Graphical Solution EMBDF

As an example, to introduce the methods of solving trigonometric equations, consider

sin θ = 0, 5 (17.1)

As explained in previous Grades,the solution ofEquation 17.1 is obtained by examining the intersect-

ing points of the graphsof:

y = sin θ

y = 0, 5

Both graphs, for− 720 ◦< θ < 720 ◦, are shown in Figure 17.9 and the intersection points of the graphs

are shown by the dots.

1

− 1

720 630 − 540 − 450 − 360 − 270 − 180 − − 90 − 90 180 270 360 450 540 630 720

�� �� �� ��

y = 0, 5

y = sin θ

Figure 17.9: Plot of y = sin θ and y = 0, 5 showing the points of intersection, hence the solutions to

the equation sin θ = 0, 5.

In the domain for θ of− 720 ◦< θ < 720 ◦, there are eight possible solutions for the equation sin θ =

0 , 5. These are θ = [− 690 ◦;− 570 ◦;− 330 ◦;− 210 ◦;30◦;150◦;390◦;510◦]