KEVOS® MAKEOS · Mathematics
Trigonometric and Involute Functions
What are the trigonometric, versed and involute functions of this angle, or the angle for an involute value?
Sine, cosine, tangent, cotangent, secant, cosecant, versed sine and cosine, and the involute function of an angle, or the angle whose involute is a given value (inverse involute) for gear work.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Calculate | choice | Find functions of an angle, or the angle for an involute value. |
| Angle | ° | Angle in degrees. |
| Involute value | Involute function value (inv α = tan α − α). |
Method and formulas
- inv α = tan α − α (α in radians).
- Versed sine = 1 − cos α; versed cosine = 1 − sin α.
- Inverse involute solved by Newton’s method.
- Example: inv 20° = 0.01490438.
Limitations
- The involute is defined for 0° ≤ α < 90°.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Replace printed trig and involute tables
- Find pressure angles from involute values in gear calculations
- Check versed sine for chord heights
Who it is for
- Engineers
- Technicians
- Engineering students
What you get
- Sine, cosine, tangent, cotangent, secant, cosecant
- Versed sine and versed cosine
- Involute, or the angle from an involute
Interpreting the result
- Versed sine × radius gives the height of an arc above its chord.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 95–114. Topic reference; no source tables or recommended settings are reproduced.
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