Question

Find a positive angle less than 360 degrees or 2pi that is coterminal with 19pi/6

Answer 1

`180\text{ \degree or }\pi\text{ radians}`

Step-by-step explanation

Coterminal angles19 are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side

for instantce

tne angle -30 and angle 330 are coterminal

so

Step 1

Let

`\text{angle}=(19)/(6)\pi`

now, draw the angel

remember that:

`\pi\text{ rad= 180 \degree}`

so, convert the angle ( from radians to degrees)

`\begin{gathered} \text{angle}=(19)/(6)\pi \\ \text{angle}=(19)/(6)\pi\cdot(\frac{180\text{ \degree}}{\pi\text{ rad}})=(18)/(6)\cdot180 \\ \text{angle}=540\text{ \degree} \end{gathered}`

hence, 540 ° is the angle

Step 2

now, as we have an angle greater than 360 and smaller than 720

to find the cotermiinal angle, we need to subtract 360 from teh given angle,so

`\begin{gathered} \cot er\min al\text{ angle= 540 \degree-360\degree} \\ \text{ coterminal angle=180 \degree} \end{gathered}`

so, 180 ° is a positive angle less than 360 ° that is coterminal with 19 pi/6

finally, let's convert the answer into radians, so

`180\text{ \degree(}\frac{\pi\text{ radi}}{180\text{ \degree}}\text{)=}\pi\text{ radians}`

therefore the answer is

`180\text{ \degree or }\pi\text{ radians}`

I hope this helpsy ou