What is the reference angle in degrees for $\frac{31 π}{6}$ $(31pi)/6$ ?

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What is the reference angle in degrees for $\frac{31 π}{6}$ $(31pi)/6$ ?

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Answer 1 · 2018-03-18T03:50:57

$\frac{7 π}{6}$ $(7pi)/6$

Explanation:

A circle is comprised of $360^{o}$ $360^o$ . In order to find the reference angle, we need to reduce the current angle to an angle that is between $0^{o}$ $0^o$ and $360^{o}$ $360^o$ .

We start with $\frac{31 π}{6}$ $(31\pi)/6$ .

We know that $0^{o} = \frac{0 π}{6}$ $0^o = (0pi)/6$ and $360^{o} = 2 π = \frac{12 π}{6}$ $360^o=2pi =(12pi)/6$

Since $360^{o} = 2 π$ $360^o = 2pi$ radians, we will subtract of $2 π = \frac{12 π}{6}$ $2pi=(12pi)/6$ each iteration:

Iteration 1:
$\frac{31 π}{6} - \frac{12 π}{6} = \frac{19 π}{6}$ $(31pi)/6 - (12pi)/6 = (19pi)/6$

Iteration 2:
$\frac{19 π}{6} - \frac{12 π}{6} = \frac{7 π}{6}$ $(19pi)/6 - (12pi)/6 = (7pi)/6$

Since $0 \leq \frac{7 π}{6} \leq \frac{12 π}{6}$ $0 \leq (7pi)/6 \leq (12pi)/6$ , we can stop as we have found the reference angle.

The reference angle is $\frac{7 π}{6}$ $color(green)((7pi)/6)$ .

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What is the reference angle in degrees for $\frac{31 π}{6}$ $(31pi)/6$ ?

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What is the reference angle in degrees for $\frac{31 π}{6}$ $(31pi)/6$ ?