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amcgough
amcgough14-Alexandrite
14-Alexandrite
Nov 14, 2026 1:31 AM UTC

How Do I Make Mathcad Trigonometric Functions Use Degrees Instead of Radians?

Scenario / Question

I'm working on problems where all the angles are in degrees, and I want the trigonometric functions to read them that way. Converting every angle to radians before each expression is evaluated is a lot of work. Can I add a statement or preference so that Mathcad evaluates trigonometric functions with degree arguments?

Overview

No. Mathcad has no setting that changes the default angle unit from radians, so trigonometric functions always treat a unitless argument as radians. Instead, attach the deg (or °) unit to each angle, or define your own trigonometric function that converts degrees for you. If you use the symbolic engine, you also need to define deg yourself, because symbolics do not recognise units.

Step-by-Step

Option 1: Attach the degree unit to each angle

  1. Add the deg unit to the argument: Type the angle followed by deg or °, for example sin(90 deg). The result is 1.
  2. Show inverse results in degrees: Evaluate an inverse function such as asin(1), then type deg in the unit placeholder to see the result as 90 deg instead of radians.

Option 2: Define a degree-based trigonometric function

  1. Create your own function: Define a function that multiplies its argument by deg before calling the built-in function, for example sind(x) := sin(x·deg).
  2. Use the new function: Call sind(30) with plain degree values, and the conversion happens automatically.

Option 3: Use degrees with the symbolic engine

  1. Define the degree unit yourself: Enter deg := π/180 and/or ° := π/180 before your symbolic expressions.
  2. Evaluate symbolically: Symbolic results with deg or ° now treat the angle correctly instead of as an unknown variable.

Key Notes & Limitations

  • Mathcad has no option or preference to change the default angle unit to anything other than radians.
  • Angles are handled like other units: write deg or ° for degrees, just as you write ft instead of m for a length.
  • The radian is dimensionless (rad = 1), so a unitless angle is always read as radians.
  • The symbolic engine does not recognize units. Without your own definition, it treats deg or ° as an unknown variable.

Related Questions (FAQ)

Q: Why does Mathcad give a different sine value than my calculator?

A: Mathcad reads a unitless argument as radians. Add deg inside the parentheses, for example sin(12.414 deg), to match a calculator set to degree mode.

Q: Can I change Mathcad's default angle unit to degrees?

A: No. There is no setting for this. Attach deg to each angle, or define a degree-based version of the function.

Q: Why does deg show up as an undefined variable in symbolic results?

A: The symbolic engine does not recognize units. Define deg := π/180 (and ° := π/180 if you use the degree symbol) before your symbolic expressions.

Links & Resources

This article is part of a new community content management program to bring more visibility to popular posts on the community.  It has been reviewed for accuracy by Andy McGough, Product Management Director.

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