"Published in Newark, California, USA"
Solve for the unknown angle for
Solution:
Consider the given equation
As you notice that the coefficients of Sin 2θ and Cos 2θ are not equal. If you will expand the above equation in order to convert the double angles into single angles, the above equation will be more complicated and it will be hard to simplify and solve the equation. Don't worry, we have a solution or technique to solve this kind of trigonometric equation.
Draw a right triangle to represent the coefficients of Sin 2θ and Cos 2θ. The coefficient of Sin 2θ will be the adjacent side of a right triangle. The coefficient of Cos 2θ will be the opposite side of a right triangle. Solve for the hypotenuse and get the trigonometric functions as follows
 |
| Photo by Math Principles in Everyday Life |
From the given equation
Divide both sides of the equation by the hypotenuse which is 2 as follows
Substitute the coefficients of Sin 2θ and Cos 2θ by their equivalent trigonometric functions as follows
but
The above equation becomes
where n = number of revolutions.