Let and be two angles measured in radians.

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Let

\alpha

and

\beta

be two angles measured in radians. (i) Prove that

\alpha

and

\beta

have the same terminal side in standard position if and only if

\beta - \alpha = 2k\pi

for some integer

k

. (ii) Taking

\theta = 190^{\circ}

, list all angles coterminal with

\theta

that lie in the interval

-1080^{\circ} \leq \phi \leq 1080^{\circ}

. (iii) How many distinct angles did you list in part (ii)? Justify your count.