Question

Which of the following statements is not true concerning radian​ measure? Select the correct choice below.

A. An angle in standard position having a radian measure of theta equals negative StartFraction 5 pi Over 3 EndFraction has a terminal side that lies in Quadrant I.
B. An angle in standard position having a radian measure of theta equals negative StartFraction 11 pi Over 6 EndFraction has a terminal side that lies in Quadrant IV.
C. One radian is the measure of a central angle that has an intercepted arc equal in length to the radius of the circle.
D. One radian is approximately 57.3 degrees.

Answer 1

B

Explanation:

Let's examine and comment on each alternative.

A. An angle with a measure of
`(-5\pi )/(3) rad` which is equivalent to -300º, will be traced in a clockwise way. As shown in the picture below. So the endpoint stops in the Quadrant I. True

B. Since
`(-11\pi )/(6)` rad is also equivalent to -330º, it has a negative orientation which tells us that it will be traced in a clockwise way as well. But its endpoint will lie on Quadrant I. Not on Quadrant IV as the B affirms.

So the B item is False.

C. Keep in mind, that Radian is a unit of measurement taken when you have an arc subtended from a unit circle with arc length 1

As shown in the picture below. True

D. If you consider the 1 Circle and its circunference, which is 2
`\pi`, (360º) we can just make this simple division:

`(360)/(2\pi ) =(180)/(\pi )` = 180º/3.1415.. ≅ 57.3º True