Solving Trigonometric Equations, 9

Category: Trigonometry

"Published in Vacaville, California, USA"

Solve for the value of x for the equation:

Solution:

Consider the given equation above 

Did you notice that all angles of the trigonometric functions are different? You can convert the multiple angles into single angles by the sum and difference of two angles formula but the equation will be more complicated. In this case, we will use the sum and product formula as follows

Take the inverse cosine on both sides of the equation, we have

                                                          or

Therefore, the values of x are

where n is the number of revolutions.