Mathematics

Problem

Consider the family of angles whose radian measure is given by

\displaystyle \beta_n = \dfrac{(3n+1)\pi}{6}

, where

n

is any integer. a. (i) Express

\beta_n

in degree measure in terms of

n

. b. (ii) Determine all integers

n

for which

\beta_n

lies in the fourth quadrant. c. (iii) For each integer obtained in part (ii), evaluate

\tan \beta_n

without using a calculator.