Secant Calculator

The secant calculator evaluates the trigonometric secant function for an angle measured in degrees or radians. Secant, commonly written sec(x), is the reciprocal of cosine. That means the calculator first interprets the angle in the selected unit, finds its cosine, and then divides one by that value. This direct relationship makes secant useful anywhere cosine appears in a denominator, including geometry, wave analysis, navigation, surveying, and calculus. Degrees divide a full turn into 360 equal parts, while radians describe angles by the ratio of arc length to radius. Both systems represent the same rotation. If you choose degrees, the calculator converts your entry to radians before using the standard trigonometric function. If you already have a radian value, select Radians and enter it directly. For reference, 180 degrees equals pi radians, 60 degrees equals pi divided by 3 radians, and 360 degrees equals 2 pi radians. Secant is undefined whenever cosine equals zero. These points occur at 90 degrees plus any whole-number multiple of 180 degrees, or at pi divided by 2 plus any whole-number multiple of pi radians. Near those angles, cosine becomes extremely small, so secant grows very large in magnitude. The calculator identifies values effectively at these vertical asymptotes and reports that the result is undefined rather than displaying an unstable floating-point value. Several familiar angles provide useful checks. The cosine of 0 degrees is 1, so its secant is 1. The cosine of 60 degrees is one half, making secant equal to 2. At 180 degrees cosine is negative 1, so secant is negative 1. Secant also has a period of 360 degrees, or 2 pi radians, meaning that adding a full rotation does not change the result. Use this calculator when checking homework, evaluating an expression, comparing degree and radian inputs, or exploring the secant graph. Results are rounded for readable display while the underlying calculation uses JavaScript double-precision arithmetic. Because values near an undefined point can change rapidly, retain enough angle precision and confirm the intended unit before interpreting a very large answer.