Trigonometric inequalities are inequalities that involve trigonometric functions, such as sine, cosine, and tangent. They often involve finding the range of values for which the inequality is true.
To solve trigonometric inequalities, you can use algebraic techniques, such as factoring and finding common denominators, as well as properties of trigonometric functions, such as the unit circle and the periodicity of functions. You can also use graphing techniques to visualize the solutions.
Some common mistakes when solving trigonometric inequalities include forgetting to check for extraneous solutions, using the wrong interval notation, and forgetting to consider the periodicity of trigonometric functions. It is important to double check your work and make sure it aligns with the given inequality.
Inclusive solutions, where the endpoint values are included in the solution set, are represented with a ≤ or ≥ sign. Exclusive solutions, where the endpoint values are not included, are represented with a < or > sign. It is important to pay attention to the given inequality and use the correct notation when expressing your final solution.
While a calculator can be helpful in graphing and visualizing solutions to trigonometric inequalities, it is important to remember that it is not a substitute for understanding the concepts and techniques used to solve them. It is always recommended to show your work and use the calculator as a tool, rather than relying on it solely for the solution.