High School Trigonometric Identity Verifier
Enter expressions for the Left Side (LHS) and Right Side (RHS) to visually and numerically verify if they are identical.
Tip: Use ‘x’ as the variable. Supports sin, cos, tan, sec, csc, cot, etc.
Verdict
Sample Checks
Status
Ready to calculate.
Graph Comparison
How the Trigonometric Identity Verifier works
A trigonometric identity is an equality that holds true for all values of the variable where both sides of the equation are defined. This distinguishes it from a conditional equation, which is only true for specific values. For example, sin(x) = 0.5 is an equation (true only at specific angles), whereas sin²(x) + cos²(x) = 1 is an identity (always true).
Numerical Verification
This tool employs numerical analysis to verify identities. It samples the functions entered on the Left Hand Side (LHS) and Right Hand Side (RHS) across a range of x-values. If the outputs match consistently (within a tiny margin of error to account for computer floating-point precision), the tool flags the expression as a potential identity.
Graphical Confirmation
In addition to number crunching, visualizing the functions is a powerful way to understand identities. If two expressions are identical, their graphs will overlap perfectly. Our tool plots the LHS as a solid blue line and the RHS as a dashed red line. If you see a single line with alternating colors or the dashed line sitting perfectly on top, the identity holds.
Why use a Trigonometric Identity Verifier?
Students often struggle with simplifying trigonometric expressions. By using this tool, you can check if your simplified result matches the original complex expression. It acts as an instant feedback mechanism for homework and study, allowing you to experiment with reciprocal, quotient, and Pythagorean identities confidently.
FAQ
No. It provides numerical and graphical evidence. A formal mathematical proof requires algebraic manipulation steps, which this tool helps you verify but does not generate.
You can type standard abbreviations like csc(x), sec(x), or cot(x).
Yes! You can enter complex fractions like (1 – cos(x)) / sin(x).
Some functions like tan(x) have asymptotes (go to infinity). The grapher tries to handle these, but vertical lines may sometimes appear near undefined points.