There are some rules which are followed while Solving Trigonometric Equations:
Rule 1: If a trigonometric equation is y = sin(x) then it will have two solutions, if equation is in the form y = sin (2x) then it will have three solutions and so on.
Rule 2: In order to solve equations we should know in which quadrant angle lies. There are 4 quadrants from top right to bottom right.
Rule 3: When we solve trigonometric equations we should know how to transform a function from one form to another. This will help to solve equations easily. We can convert a sine function in cosine function, in tangent function and vice versa.
Rule 4: In order to solve such trigonometric equations we should know angle values. We can also convert angle value in other angle by adding or subtracting 180 degree or 90 degree.
Rule 5: By making a graph and locating angles on it we can easily calculate trigonometric equations. We mark location in one of four quadrants.
Rule 6: All Trigonometric Functions are periodic in nature, which means they will repeat their values after a certain time Period. They will follow same values again. We can predict their value with help of this rule.
These are some rules which help to solve trigonometric equations.