Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.4

is solved as

sin θ = 0, 5

= 30◦

On your calculator youwould type sin−^1 ( 0 , 5 ) =to find the size of θ.

This step does not needto be shown in your calculations.

Example 7:

QUESTION

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

trigonometric functions.

SOLUTION

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

on one side of the equation. Then solve for theangle using the inversefunction.

tan θ + 0,5 = 1, 5

tan θ = 1

= 45◦

Trigonometric equationsoften look very simple.Consider solving the equation sin θ = 0, 7. We can
take the inverse sine ofboth sides to find that θ = sin−^1 (0,7). If we put this into a calculator we find
that sin−^1 (0,7) = 44, 42 ◦. This is true, however, it does not tell the wholestory.

y

x

1

− 1

360 − 180 − 180 360

Figure 17.10: The sine graph. The dotted line represents y = 0, 7. There are four points of intersection
on this interval, thus four solutions to sin θ = 0, 7.

As you can see from Figure 17.10, there are four possible angles with a sine of 0 , 7 between− 360 ◦and
360 ◦. If we were to extend the range of the sine graphto infinity we would in fact see that there are an