A trigonometric equation is an equation that includes one or more trigonometric functions, such as sine, cosine, or tangent. These equations involve finding the value of an unknown angle or side length in a triangle.
The possible solutions of a trigonometric equation depend on the type of equation and the given restrictions. For example, a basic trigonometric equation may have infinite solutions, while a trigonometric equation with specific restrictions may have a finite number of solutions.
To find the range of possible solutions of a trigonometric equation, you can use a variety of methods such as factoring, graphing, or using trigonometric identities. It is important to pay attention to any given restrictions or domain limitations when finding the range of solutions.
Some common mistakes when solving trigonometric equations include forgetting to account for the period or amplitude of the function, making calculation errors, or not properly applying trigonometric identities. It is important to carefully follow the steps and check your work when solving these equations.
You can check if your solution is correct for a trigonometric equation by plugging it back into the original equation and simplifying. If the resulting value is equal to the other side of the equation, then your solution is correct. Another way to check is by using a graphing calculator to see if your solution lies on the graph of the equation.