Everything Maths Grade 11

17.4 CHAPTER 17. TRIGONOMETRY

Example 6:

QUESTION

Find θ, if tan θ + 0,5 = 1, 5 , with 0 ◦< θ < 90 ◦. Determine the solutiongraphically.

SOLUTION

Step 1 : Write the equation sothat all the terms with the unknown quantity (i.e. θ) are

on one side of the equation.

tan θ + 0,5 = 1, 5

tan θ = 1

Step 2 : Identify the two functions which are intersecting.

y = tan θ

y = 1

Step 3 : Draw graphs of bothfunctions, over the required domain and identify the

intersection point.

0

1

− 1

90

� y = 1

y = tan θ

45

The graphs intersect at θ = 45◦.

Algebraic Solution EMBDG

The inverse trigonometric functions can be usedto solve trigonometric equations. These may be shown
as second functions onyour calculator: sin−^1 , cos−^1 and tan−^1.

Using inverse trigonometric functions, the equation

sin θ = 0, 5