Solving Trigonometric Equations

Trigonometry is defined as its own entity which constitutes the relation between angles and sides of a triangle. It is a branch of mathematics and defines various Relations which can be formed by the possible angles and sides of the triangle. Trigonometric equations are the equations which consist of various trigonometric Functions. In these equations either the value of the sides or the angles are to be determined. There are various trigonometric Functions:
Sine, cosine, sec, cosec, tan, cot. Sine function is defined as the Ratio of perpendicular and hypotenuse. Cosine function is defined as the ratio of base and hypotenuse. Sec is the ratio of hypotenuse and base. Tan is the ratio of perpendicular and base and cot function is defined as the ratio of base and perpendicular.
Solving Trigonometric Equations is quiet important task in Trigonometry, as various Trigonometric Functions may not be defined. We can solve trigonometric equations by simply solving it using basic solving techniques.
There are four quadrants defined as first, second, third and fourth quadrant.
The first quadrant is positive for all trigonometric functions and lies between 0 to 90⁰. The second quadrant lies between 90⁰ and 180⁰ and is positive for sine and cosec functions. The third quadrant lies from 180 to 270 and is positive for tan and cot functions. And the last quadrant lies between 270 and 360 which are positive for cos and sec functions. Its figure is shown below:
  
Let’s take an example for solving trigonometric equations:
Suppose we need to solve the equation 2 sin x – 2 = 0. For solving the equation firstly use simple mathematics and then apply logics considering quadrants. From the above equation we get, sin x =1. And value of sin is 1 at 90⁰. Therefore value of x is equals to 1. Since it lies in first quadrant, therefore value will be positive as first quadrant gives positive values of all the functions.