manish00333 said:So, pi/4 + 2pi = 9pi/4
and 3pi/4 + 2pi = 11pi/4
and when i divide them by 2, i get 9pi/8 and 11pi/8.
A trigonometric equation is an equation that involves the use of trigonometric functions such as sine, cosine, tangent, etc. These equations are used to solve for unknown angles or sides in a triangle, or to represent periodic phenomena in mathematics and science.
To solve a trigonometric equation, you must first isolate the trigonometric function on one side of the equation. Then, use inverse trigonometric functions or trigonometric identities to simplify the equation and solve for the unknown variable.
Some common trigonometric identities used in solving equations include the Pythagorean identities, double angle identities, half angle identities, and sum and difference identities. These identities allow you to rewrite trigonometric functions in terms of other functions to simplify equations.
Yes, there are special cases when solving trigonometric equations, such as when the equation involves trigonometric functions with different periods or when solving for multiple solutions. In these cases, it is important to use the appropriate trigonometric identities and consider all possible solutions.
Trigonometric equations have many practical applications in fields such as physics, engineering, and navigation. They are used to model and analyze periodic phenomena, such as sound waves and alternating currents, and to solve problems involving angles and distances in real-world situations.