Simple Trigonometric EquationsSimple Trigonometric Equations

The sine graph below illustrates that there are many solutions to the trigonometric equation sin x = 0.5.

5We know that and are two particular solutions of sin 0.5

6 6x x x

Since the period of sin is 2 , we can add integral multiples of 2

to get the other solutions.

x

52 and 2

6 6x n x n

When solving an equation such as sin x = 0.6, we can use a calculator .

Example 1. Find the values of between 0 and 2 for which sin 0.6.x x Set your calculator in radian mode.

1sin 0.6x 0.6435

This means that 0.6435 is the reference angle for other solutions.

Since x is positive, and sine is positive in the first and second quadrants, - 0.6435 is also a solution.So 2.4981 is also a solution.x

To solve an equation involving a single trigonometric function, we first transform the equation so that the function is alone on one side of the equals sign.

2. To the nearest tenth of a degree, solve 3cos 9 7 for 0 360

3cos 9 7 3cos 2

2cos

3

1 2cos 48.2

3

This is the reference angle

Cos is negative in the second quadrant so 180 48.2 131.8

Cos is also negative in the third quadrant so 180 48.2 228.2

Inclination and SlopeInclination and Slope

Example 3. To the nearest degree,

find the inclination of the line 2 5 15.x y