Cofunction Calculator Radians

Cofunction Identities:

\[ \sin(\theta) = \cos\left(\frac{\pi}{2} - \theta\right) \] \[ \cos(\theta) = \sin\left(\frac{\pi}{2} - \theta\right) \] \[ \tan(\theta) = \cot\left(\frac{\pi}{2} - \theta\right) \] \[ \cot(\theta) = \tan\left(\frac{\pi}{2} - \theta\right) \] \[ \sec(\theta) = \csc\left(\frac{\pi}{2} - \theta\right) \] \[ \csc(\theta) = \sec\left(\frac{\pi}{2} - \theta\right) \]

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1. What Are Cofunction Identities?

Cofunction identities show the relationship between trigonometric functions and their complementary angles (π/2 - θ in radians). These identities demonstrate that any trigonometric function of an angle is equal to the cofunction of its complement.

2. How Does the Calculator Work?

The calculator demonstrates all six cofunction identities:

Explanation: For any angle θ (in radians), the function value equals the cofunction of its complement (π/2 - θ).

3. Importance of Cofunctions

Details: Cofunction identities are fundamental in trigonometry, used in simplifying expressions, solving equations, and proving other trigonometric identities.

4. Using the Calculator

Tips: Enter any angle in radians to see all six cofunction relationships demonstrated numerically. The calculator shows both sides of each identity.

5. Frequently Asked Questions (FAQ)

Q1: Why are these called "cofunctions"?
A: They're called cofunctions because they represent function pairs (sine/cosine, tangent/cotangent, secant/cosecant) that relate to complementary angles.

Q2: Do these identities work in degrees?
A: Yes, but the complement would be (90° - θ) instead of (π/2 - θ). This calculator specifically uses radians.

Q3: What's the practical use of cofunction identities?
A: They're used in calculus, physics, engineering, and anywhere trigonometric relationships between complementary angles are needed.

Q4: Can I use this for any angle?
A: Yes, though results may be undefined for angles where functions approach infinity (like π/2 for tangent).

Q5: How are these identities derived?
A: They come from the right triangle definitions of trigonometric functions and the relationship between angles in a right triangle.