Everything Maths Grade 10

Worked example 9: Solving trigonometric equations

QUESTION

Find the value ofif 3 sin=2,4.

SOLUTION

Step 1: Rearrange the equation

We need to rearrange the equation so thatsinis on one side of the equation.

3 sin=2,4

sin=

2,4

3

Step 2: Use your calculator to solve for

To solve for, you will need to use the inverse sine function on your calculator. This works backwards by using
the ratio of the sides to determine the angle which resulted in that ratio.

Press SHIFT sin ( 2. 4 ÷ 3 ) = 53,1301...53,13.

Step 3: Write the final answer

53,13°

NOTE:

When you are solving trigonometric equations you might find that you get an error when you try to calculate

sinorcos(remember that both the sine and cosine functions have a maximum value of 1). For these cases

there is no solution to the equation.

Worked example 10: Solving trigonometric equations

QUESTION

Solve for : 3 sec =1,4.

SOLUTION

Step 1: Convertsectocos

There is no “sec” button on the calculator and so we need to convertsectocosso we can find.

3 sec =1,4

3

cos

=1,4

Step 2: Rearrange the equation

We need to rearrange the equation so that we havecos on one side of the equation.

3

cos

=1,4

3 =1,4cos

3

1,4

=cos

Chapter 5. Trigonometry 129