Mathematics

Problem

Define

g(\theta)=\dfrac{\sin \theta}{1+\cos \theta}

for real

\theta

. a. (i) Find all values of

\theta

in the open interval

(0,\,2\pi)

for which

g(\theta)

is not defined. b. (ii) Rewrite

g(\theta)

in terms of

\tan\dfrac{\theta}{2}

. c. (iii) Using the result of part (ii), determine the range of

g

for all permissible values of

\theta