Trig Identity Calculator

Trigonometric identities are the web of equalities that tie the six trig functions together, and this calculator both evaluates those functions at any angle and checks the most important identities for you numerically. Enter an angle, choose degrees or radians, and it returns the sine, cosine, tangent, cosecant, secant and cotangent of the angle, then verifies the fundamental identities by computing both sides and showing they agree. That includes the reciprocal relationships, where cosecant is one over sine, secant is one over cosine and cotangent is one over tangent, the quotient identities, where tangent is sine over cosine, and above all the Pythagorean identities, the cornerstone results that sine squared plus cosine squared equals one, that one plus tangent squared equals secant squared, and that one plus cotangent squared equals cosecant squared. Seeing these confirmed with real numbers is a genuinely effective way to learn and remember them, because identities are notoriously easy to misremember or rearrange the wrong way, and a quick numerical check at a known angle catches mistakes before they propagate into a proof or an equation. The tool is a natural companion for NCEA and senior trigonometry and first-year university maths, useful for checking homework, exploring how the functions and their reciprocals behave as the angle changes, and confirming a rearranged identity is still true. It also helps build intuition for special angles, such as why tangent is undefined at 90 degrees, where cosine is zero, or why the functions repeat every full turn. Because everything recalculates as you type, you can move the angle around and watch the identities hold at every value. The identities and a worked example are explained clearly below.

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