Complementary Angle Theorem Calculator

Complementary Angle Theorems:

\[ \sin(90° - θ) = \cos θ \] \[ \cos(90° - θ) = \sin θ \] \[ \tan(90° - θ) = \cot θ \] \[ \cot(90° - θ) = \tan θ \] \[ \sec(90° - θ) = \csc θ \] \[ \csc(90° - θ) = \sec θ \]

Result:

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1. What is the Complementary Angle Theorem?

The Complementary Angle Theorem states that the trigonometric function of an angle is equal to the cofunction of its complement. Two angles are complementary if they add up to 90 degrees.

2. How Does the Calculator Work?

The calculator demonstrates the complementary angle relationships:

\[ \sin(90° - θ) = \cos θ \] \[ \cos(90° - θ) = \sin θ \] \[ \tan(90° - θ) = \cot θ \] \[ \cot(90° - θ) = \tan θ \] \[ \sec(90° - θ) = \csc θ \] \[ \csc(90° - θ) = \sec θ \]

Explanation: These identities show the relationship between trigonometric functions and their cofunctions for complementary angles.

3. Importance of Complementary Angles

Details: Understanding complementary angle relationships is fundamental in trigonometry, helping simplify expressions and solve trigonometric equations.

4. Using the Calculator

Tips: Enter an angle between 0° and 90°, select a trigonometric function, and the calculator will show both the direct calculation and its complementary equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What are complementary angles?
A: Two angles are complementary when their measures add up to 90 degrees.

Q2: What are cofunctions?
A: Cofunctions are function pairs like sine/cosine, tangent/cotangent, and secant/cosecant that are related through complementary angles.

Q3: Does this work in radians?
A: Yes, but the angles must add to π/2 radians (equivalent to 90°).

Q4: Why are these identities useful?
A: They allow simplification of trigonometric expressions and solving equations by converting between functions.

Q5: Can these be extended to other angle relationships?
A: Similar relationships exist for supplementary angles (sum to 180°), but with sign changes for some functions.