Trig Identity Verifier

Verify sin²θ + cos²θ = 1 and more

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About Trig Identity Verifier

A trigonometric identity verifier that evaluates sin, cos, tan, csc, sec, cot at any angle (degrees or radians). Compares both sides of common identities like sin²θ+cos²θ=1, verifies Pythagorean, reciprocal, and double-angle identities. All calculations are client-side. Essential for trigonometry, calculus, and physics.

Trig Identity Verifier Features

  • All 6 functions
  • Identity check
  • Deg/Rad
  • Pythagorean
  • Double angle
Trigonometric identities are equations true for all valid angles. Pythagorean: sin²θ+cos²θ=1. Reciprocal: cscθ=1/sinθ. Double angle: sin2θ=2sinθcosθ. These identities simplify expressions and solve equations. Verifying them numerically confirms understanding.

How to Use

Enter an angle:

  • Angle: In degrees or radians
  • Functions: All 6 trig values
  • Identities: Verified at your angle

Pythagorean Identities

  • sin²θ + cos²θ = 1
  • 1 + tan²θ = sec²θ
  • 1 + cot²θ = csc²θ

Double Angle

  • sin(2θ) = 2sinθcosθ
  • cos(2θ) = cos²θ − sin²θ
  • tan(2θ) = 2tanθ/(1−tan²θ)

Step-by-Step Instructions

  1. 1Enter an angle value.
  2. 2Toggle degrees/radians.
  3. 3View all 6 trig functions.
  4. 4Check identity verifications.
  5. 5Try special angles.

Trig Identity Verifier — Frequently Asked Questions

Why does sin²θ+cos²θ always equal 1?+

On the unit circle, a point has coordinates (cosθ, sinθ). By the Pythagorean theorem, x²+y²=r²=1. So cos²θ+sin²θ=1 for any angle.

What are the special angles?+

0°, 30°, 45°, 60°, 90° (and their equivalents). These have exact trig values involving √2, √3, and fractions. 45°: sin=cos=√2/2.

When would I need to verify an identity?+

In calculus for simplifying integrals and derivatives, in physics for wave equations, in engineering for signal processing, and in math exams!

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