Cosecant, Secant & Cotangent Calculator

How it is calculated

The angle is entered in degrees and converted to radians. The tool then computes csc θ = 1 ÷ sin θ, sec θ = 1 ÷ cos θ and cot θ = cos θ ÷ sin θ, each shown to 6 decimal places as a unitless ratio. Negative angles and angles above 360° work, because the functions repeat every 360° (390° gives the same values as 30°). Only the function that is truly undefined is blanked and shown as a dash: csc and cot when sin θ is practically zero (0°, 180° and their multiples), and sec when cos θ is practically zero (90°, 270°). The other values are still given, so at 90° you get csc = 1.000000, sec = — and cot = 0.000000. An empty box gives nothing.

Common mistakes

• Confusing the reciprocal with the inverse function. sec θ is 1 ÷ cos θ, whereas arccos gives an angle; 1.154701 here is a ratio, not 30°.
• Entering radians. 1.5708 is treated as 1.5708 degrees, not as a right angle.
• Reading a dash as an error. At 0° and 180° cosecant and cotangent are undefined, and at 90° and 270° the secant is, so the tool shows a dash for exactly those and still gives the rest.
• Pairing the wrong function with its base. Cosecant goes with sine and secant goes with cosine, which is easy to reverse because the names look the wrong way round.
• Expecting values between −1 and 1. Secant and cosecant are never inside that range; their size is always 1 or more, while cotangent can be any number.