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

[mathdad]

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.

 

[skeeter]

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 $\dfrac{7\pi}{6} - \pi = \dfrac{\pi}{6}$

 

[mathdad]

Is there an algebraic method for finding the reference number, reference angle and coterminal angle?

 

[skeeter]

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

 

[mathdad]

The author of the textbook said that "reference angle" is typically used when referring to degrees and "reference number" when referring to radian.