Mathematics

Problem

Consider the equation

3\theta^{\circ}+\frac{\theta}{2}=\frac{5\pi}{6},

where

\theta^{\circ}

denotes

\theta

measured in degrees and

\theta

(without the symbol) is measured in radians. a. (i) Express

3\theta^{\circ}

in radian measure. b. (ii) Solve the resulting equation for

\theta

. c. (iii) Express the value of

\theta

obtained in part (ii) in degrees and minutes, correct to the nearest minute.