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

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The discussion revolves around finding the reference number for the angle -5π/6. The calculated reference number is -π/6, but the textbook states it should be π/6. A coterminal angle is determined as 7π/6, which leads to a reference angle of π/6. Participants clarify that a reference angle is the acute angle formed with the x-axis, while the term "reference number" is less commonly used. The conversation highlights the distinction between reference angles and coterminal angles in trigonometry.
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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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