Versine Calculator

What Is the Versine Function?

The versine function (commonly written as \( \text{versin}(\theta) \)) is a historical trigonometric function that represents the complementary value of the cosine function. The formula for the versine function is: \( \text{versin}(\theta) = 1 - \cos(\theta) \) This means the versine measures the deviation or offset from the cosine value.

For \( \theta = 60^\circ \): \( \text{versin}(60^\circ) = 1 - \cos(60^\circ) = 1 - 0.5 = 0.5 \)

Graph of the Versine Function

The versine function's graph appears as a sine wave with a positive vertical shift.

• Periodicity: Periodicity
• Domain: Defined for all real numbers \( \mathbb{R} \).
• Range: \( \text{versin}(\theta) \in [0, 2] \).
• Amplitude: Maximum value is \( 2 \), and minimum value is \( 0 \).
• Wave Characteristics: Reaches a minimum value of \( 0 \) at \( \theta = 0 \) and \( \theta = 2\pi \). Reaches a maximum value of \( 2 \) at \( \theta = \pi \).

Versine Conversion Table