Question

Which angles are coterminal with −6π5 ? Select each correct answer. 14π/5 −16π/5 −π/5 −11π/5

Answer 1

ANSWER

$- \frac{16 \pi}{5} \: and \: \frac{14\pi}{5}$


EXPLANATION

Coterminal angles are angles in standard position that have the same terminal side.


To find an angle in standard position that is coterminal with

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

We add or subtract multiples of
$2 \pi$

The first addition gives,

$- \frac{6 \pi}{5} + 2 \pi = \frac{4 \pi}{5}$


We add the second multiple to get,

$- \frac{6 \pi}{5} +2( 2 \pi )= \frac{14 \pi}{5}$

Since this is the maximum value among the options, we end the addition here.


Let us now subtract the first multiple to get,


$- \frac{6 \pi}{5} - 2 \pi = - \frac{16 \pi}{5}$


We end the subtraction here because this is the least value among the options.


Therefore the angles that are coterminal with
$- \frac{6 \pi}{5}$
are

$- \frac{16 \pi}{5} \: and \: \frac{14\pi}{5}$

Answer 2

Hello!

To find the angle that is coterminal with -6π/5, we will need to add or subtract 2π to that radian measure.

Why? 2π is equal to 360 degrees which is the degrees in a circle. If it is coterminal, then it has to be on the same side of the given measure, so we can add 2π or 360 degrees to the given measure. It creates one full revolution.

-6π/5 + 2π = 4π/5 | Since this value is not an answer choice, we can subtract 2π from -6π/5.

-6π/5 - 2π = -16π/5

Therefore, the angle that is coterminal with -6π/5 is -16π/5, the second choice.