What is the reference number given -5π/6?

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Discussion Overview

The discussion revolves around the concept of finding the reference number for the angle -5π/6, including related concepts such as reference angles and coterminal angles. Participants explore both graphical and algebraic methods for determining these values.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that the reference number can be calculated graphically, resulting in r = -π/6, while the textbook states the answer is π/6.
  • One participant calculates a coterminal angle for -5π/6 as 7π/6 and identifies its reference angle as π/6.
  • Another participant questions the terminology, expressing confusion over the term "reference number" and clarifying that a reference angle is the acute angle formed with the x-axis.
  • A participant cites the textbook's distinction between "reference angle" for degrees and "reference number" for radians, suggesting a potential source of confusion.

Areas of Agreement / Disagreement

There is no consensus on the terminology used, with some participants agreeing on the mathematical concepts while others contest the use of "reference number." The discussion remains unresolved regarding the preferred terminology and the calculations presented.

Contextual Notes

Participants express uncertainty about the definitions and distinctions between reference angles and reference numbers, indicating a potential misunderstanding of terminology in the context of radians versus degrees.

Who May Find This Useful

This discussion may be useful for students studying trigonometry, particularly those grappling with the concepts of reference angles and coterminal angles in both degrees and radians.

mathdad
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Given -5π/6, find the reference number.

Let r = reference number

I decided to graph -5π/6.

r = -π - (-5π/6)

r = -π + 5π/6

r = -π/6

Book's answer for r is π/6.
 
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RTCNTC said:
Given -5π/6, find the reference number.

Let r = reference number

I decided to graph -5π/6.

r = -π - (-5π/6)

r = -π + 5π/6

r = -π/6

Book's answer for r is π/6.

1. Determine the positive angle that is coterminal with the given angle ...

$-\dfrac{5\pi}{6} + 2\pi = \dfrac{7\pi}{6}$

2. Since $\dfrac{7\pi}{6}$ is in quad III, its reference angle is $\dfrac{7\pi}{6} - \pi = \dfrac{\pi}{6}$
 
Is there an algebraic method for finding the reference number, reference angle and coterminal angle?
 
RTCNTC said:
Is there an algebraic method for finding the reference number, reference angle and coterminal angle?

don't know what you mean by a reference "number" ... never heard of it

a reference angle is the positive acute angle formed by an angle in standard position and the x-axis

two angles are coterminal if their terminal sides coincide ... they differ by an integer multiple of 360 degrees or 2pi radians
 
The author of the textbook said that "reference angle" is typically used when referring to degrees and "reference number" when referring to radian.
 

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