A trigonometric inequality is an inequality that involves trigonometric functions, such as sine, cosine, and tangent. These inequalities are typically solved for a range of values of the variable, rather than a single solution.
To solve a trigonometric inequality, you must first isolate the trigonometric function on one side of the inequality. Then, use algebraic techniques, such as factoring and the quadratic formula, to solve for the variable. Finally, graph the solution set to determine the range of values that satisfy the inequality.
A trigonometric equation has a single solution, while a trigonometric inequality has a range of solutions. Additionally, solving a trigonometric inequality may involve using algebraic techniques, while solving a trigonometric equation typically only requires finding the inverse of the trigonometric function.
Yes, you can use a calculator to help solve a trigonometric inequality. However, it is important to understand the steps involved in solving the inequality by hand before relying on a calculator.
Some common mistakes when solving trigonometric inequalities include forgetting to consider the period of the trigonometric function, not isolating the function on one side of the inequality, and not graphing the solution set to check for extraneous solutions. It is important to carefully follow each step and check your work to avoid these mistakes.