What it is
This trigonometric functions calculator computes all six trig ratios — sine, cosine, tangent, cosecant, secant, and cotangent — for an angle entered in DEGREES. The angle may be a plain decimal value (5.25) or in degrees-minutes-seconds (DMS) notation (5'12'6). It is a pure-math tool that applies identically everywhere.
How to use it
Enter your angle in the Angle field. For a decimal angle type the number directly, e.g. 45 or 5.25. For DMS, separate degrees, arc-minutes and arc-seconds with apostrophes: 5'12'6 means 5 degrees, 12 minutes, 6 seconds. Choose how many display digits you want, then read off the six ratios. Undefined values (such as tan 90 degrees) are shown as "undefined".
The formula explained
The angle in degrees is first converted to decimal degrees (degrees + minutes/60 + seconds/3600) and then to radians using θ_{rad}=θ_{deg}·((π) ÷ (180)). From sin and cos the rest follow:
The reciprocal ratios are
Reciprocal functions are undefined where their denominator is zero, so tan and sec are undefined at 90 and 270 degrees, while csc and cot are undefined at 0 and 180 degrees.
Worked example
For 5'12'6 the decimal angle is
In radians that is 0.0907866. Then \sin = 0.090661937, \cos = 0.995882104 and \tan = 0.091036699.
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