Trigonometry: What are Gradients?

  • Context: High School 
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Discussion Overview

The discussion revolves around the concept of "gradients" in trigonometry, specifically focusing on the unit of angle known as the gradian. Participants explore its definition, relationship to other angle measures, and its applications.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the meaning of "gradients" as used in calculators, noting they have not encountered the term before.
  • Another participant clarifies that "gradients" refers to gradians, defining it as a unit of angle where a full circle is 400 gradians.
  • A third participant presents a relationship between degrees, gradians, and radians, stating that 180 degrees equals 200 gradians and π radians.
  • A fourth participant emphasizes the equivalence of 90 degrees to π/2 radians and 100 gradians, explaining that "1 grad" represents 1% of a straight angle and mentioning the use of grads in measuring slopes by highway engineers.
  • There is a note of confusion regarding the terms "grad" and "gradient," as both are abbreviated the same way.

Areas of Agreement / Disagreement

Participants provide various definitions and relationships involving gradians, but there is no consensus on the terminology or its implications, particularly regarding the distinction between "grad" and "gradient."

Contextual Notes

Some participants express uncertainty about the use of the terms and their applications, indicating a potential for confusion in definitions and usage.

TSN79
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Just a simple wondering here, the calculator that comes with Windows XP (and other versions) have three choices for trigonometry, degrees, radians, and gradients. I have never heard of this last one, what is it?
 
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It's a gradian-- a unit of angle such that the angle of a full circle is 400 gradians.
 
[tex]180 \mbox{degrees} = 200 \mbox{gradients} = \pi \mbox{radians} = \mbox{Angle of a Straight Line}[/tex]
 
I think the real point is that 90 degrees= [itex]\pi/2[/itex] radians= 100 gradians. "1 grad" is 1 % of "straight up" and grads are typically used by highway engineers to measure slopes.

It is unfortunate that both "gradian" and "gradient" are abbreviated "grad"!
 

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