Coversine Calculator

What Is the Coversine Function?

The coversine function (\( \text{coversin}(\theta) \) or \( \text{versin}(\pi/2 - \theta) \)) is a lesser-known trigonometric function. It represents the complement of the sine function and can be defined as: \( \text{coversin}(\theta) = 1 - \sin(\theta) \) This formula shows that coversine is the shifted version of the sine function, useful for expressing the deviation of sine from unity.

For \( \theta = 30^\circ \): \( \text{coversin}(30^\circ) = 1 - \sin(30^\circ) = 1 - 0.5 = 0.5 \)

Graph of the Coversine Func

The coversine function forms a shifted sine wave with distinct characteristics:

• Periodicity: The coversine function has a period of \( 2\pi \).
• Domain: Defined for all real numbers \( \mathbb{R} \).
• Range: \( \text{coversin}(\theta) \in [0, 2] \).
• Amplitude: Maximum value is \( 2 \), and minimum value is \( 0 \).
• Wave Characteristics: Reaches a minimum value of \( 0 \) when \( \sin(\theta) = 1 \). Reaches a maximum value of \( 2 \) when \( \sin(\theta) = -1 \).

Coversine Conversion Table