Trig Identity Verifier
Plug in any angle and verify the fundamental trig identities numerically.
Enter Angle
Degrees
Identity Check
Enter an angle and click verify.
Fundamental trig identities
• Pythagorean: sin²θ + cos²θ = 1
• Quotient: tan θ = sin θ / cos θ
• Reciprocal: csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
• Derived: 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ
• Even/Odd: cos(−θ) = cos θ, sin(−θ) = −sin θ, tan(−θ) = −tan θ
Frequently Asked Questions
What is a trigonometric identity?▾
An equation involving trig functions that is true for every value of the variable. They're used to simplify expressions and solve equations.
What are the most important identities?▾
The Pythagorean identity sin²θ + cos²θ = 1, the quotient identity tan θ = sin θ/cos θ, and the reciprocal identities (csc, sec, cot).
How does this calculator "verify" an identity?▾
It plugs in your angle on both sides of each fundamental identity and checks the values are equal within floating-point tolerance.
Why might a check show ✗?▾
Either the identity has a true exception at your angle (e.g., a function is undefined there) or you hit the limits of floating-point precision near a singularity.