Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# Draw an angle in standard position with the given measure.$\frac{5 \pi}{6}$

Solutions

Verified
Step 1
1 of 2

In 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:

## Recommended textbook solutions #### Algebra 2 Common Core

1st EditionISBN: 9780133186024 (2 more)Basia Hall, Charles, Kennedy
7,537 solutions #### enVision Algebra 2

1st EditionISBN: 9780328931590Al Cuoco
3,573 solutions #### Big Ideas Math Algebra 2: A Common Core Curriculum

1st EditionISBN: 9781608408405 (1 more)Boswell, Larson
5,067 solutions #### Algebra and Trigonometry

1st EditionISBN: 9781938168376 (1 more)OpenStax
6,343 solutions