Draw an angle in standard position with the given measure.

$\frac{5 \pi}{6}$

Solutions

VerifiedIn standard position, the initial side of the angle lies on the positive $x$-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 $\theta$ radians, we will divide $\theta$ by a full rotation of $2\pi$ radians and then rewrite the result as a more recognizable fraction to understand where to put the terminal side.

$\dfrac{\theta \text{ rads}}{2\pi \text{ rads}}=\dfrac{ {}^{5\pi}{\mskip -2mu/\mskip -3mu}_{6} \text{ rads}}{2\pi\text{ rads}}=\dfrac{5\pi}{12\pi}=\dfrac{5}{3}\cdot \qty(\dfrac{1}{4})={\color{#c34632}1\dfrac{2}{3}\cdot \qty(\dfrac{1}{4})}$

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

Note that in the standard position:

(1) The initial line should be horizontal

(2) The positive angles are measured in the counter-clockwise direction and negative angles are measured in the clockwise direction.

The standard position for an angle with the given measure is shown below:

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