Let denote the degree measure and the radian measure of the same angle.

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let

d

denote the degree measure and

r

the radian measure of the same angle. (i) Starting from the fact that the measure of a straight angle is both

180^{\text{o}}

and

\pi

radians, derive the general relation connecting

d

and

r

. (ii) Show that if two angles differ by an integer multiple of

360^{\text{o}}

, then their radian measures differ by an integer multiple of

2\pi

. (iii) Using part (ii), list three distinct angles, all coterminal with

\dfrac{5\pi}{3}

radians, whose degree measures lie between

-1080^{\text{o}}

and

1080^{\text{o}}

. Give exact values only.