Secant Calculator

In trigonometry, the secant of an angle in a right-angled triangle is defined as the reciprocal of its cosine. Mathematically, it represents the ratio of the hypotenuse to the adjacent side. The calculator processes your input using the core equations: result = 1 / cos(angle), and automatically converts angle measurements between radians and degrees using the relation angleInDegrees = angle * (180 / pi). It also evaluates whether the angle yields a standard algebraic fraction using special angle recognition routines.

Let us calculate the secant of an angle measuring pi / 3 radians (which equals 60 degrees). First, we find the cosine of pi / 3 radians, which is 0.5. Next, we apply the secant formula by taking the reciprocal of this cosine value: result = 1 / 0.5 = 2.0. Therefore, the secant of pi / 3 radians is exactly 2, meaning the hypotenuse is twice the length of the adjacent side in this reference triangle.

Always double-check whether your input angle is formatted in degrees or radians before calculating to avoid drastic computational errors. Keep in mind that the secant function is undefined at angles where the cosine equals zero, such as 90 degrees or pi / 2 radians, which will result in an infinity or division-by-zero error. Utilize radian inputs for calculus applications and degree inputs for standard geometric drafting or structural design problems.