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Draw an angle in standard position with the given measure.

5π6\frac{5 \pi}{6}


Answered 1 year ago
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In standard position, the initial side of the angle lies on the positive xx-axis, and each quadrant represents a full quarter-rotation.

Since the given angle is positive, we will make a counterclockwise rotation.

To draw an angle of θ\theta radians, we will divide θ\theta by a full rotation of 2π2\pi radians and then rewrite the result as a more recognizable fraction to understand where to put the terminal side.

θ rads2π rads=5π/ ⁣6 rads2π rads=5π12π=53(14)=123(14)\dfrac{\theta \text{ rads}}{2\pi \text{ rads}}=\dfrac{ {}^{5\pi}{\mskip -2mu/\mskip -3mu}_{6} \text{ rads}}{2\pi\text{ rads}}=\dfrac{5\pi}{12\pi}=\dfrac{5}{3}\cdot \qty(\dfrac{1}{4})={\color{#c34632}1\dfrac{2}{3}\cdot \qty(\dfrac{1}{4})}

So, we see that 5π6\dfrac{5\pi}{6} rads is equivalent to a full quarter-rotation plus two-thirds of a quarter-rotation\text{\textcolor{#c34632}{a full quarter-rotation plus two-thirds of a quarter-rotation}}. Thus, we get the following:

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