Trigonometric Identity Proof Guide
What an Identity Means
A trigonometric identity is a statement that stays true for every allowed angle. This calculator helps users test that claim with organized checks. It compares the left side and right side across several sample angles. It also highlights common formulas that may prove the statement. The tool is useful for study, lesson planning, and quick homework review.
Why Step Checks Matter
A manual proof often begins by changing one side only. You may rewrite reciprocal functions, quotient functions, or squared expressions. Then you simplify until both sides match. This page follows that same idea. It does not replace your teacher’s required work. It gives a clear path and numerical evidence.
Expression Support
The calculator accepts expressions with sin, cos, tan, sec, csc, and cot. It also supports powers, parentheses, pi, and basic arithmetic. You can choose degree or radian mode. The sample range lets you avoid angles where one side is undefined. This matters when tangent, cotangent, secant, or cosecant appear.
Tolerance and Accuracy
Use a small tolerance for exact school identities. A tolerance such as 0.000001 works well for many problems. Larger tolerances can hide mistakes. Smaller tolerances may report tiny rounding differences. The maximum difference column shows the largest gap found.
Proof Strategy
The strongest proof usually uses identities before substitution. Important rules include reciprocal identities, quotient identities, and Pythagorean identities. For example, sec x equals one over cos x. Also, tan x equals sin x divided by cos x. These changes often turn a hard expression into a familiar one.
Reading the Table
The table below the result records every tested angle. It shows both values and their absolute difference. If a point is undefined, the calculator skips it and reports a warning. That warning may reveal a domain restriction, not a failed identity.
Saving Results
The export buttons are designed for documentation. A CSV file helps with spreadsheets. A PDF file gives a simple proof record. You can attach it to notes or keep it for revision.
Final Review
Good habits also reduce errors, especially when signs, squares, and reciprocal forms appear in the same identity during proofs.
Always finish by writing a clean proof in words. State the formulas used. Show each algebra step. Mention domain limits when needed. This calculator supports that process, but the final reasoning should still be clear.