Find the exact value of the following a 3 sin 30 degree 5 t

Find the exact value of the following: (a) 3 sin 30 degree + 5 tan(- pi/6) (b) cos(5 pi/4) - cot (pi/4) (c) sec (31 pi/6)

Solution

a) 3 sin 30 + 5 tan (-pi/6 )

sin 30 = 1/2

tan - pi/6 = - 1 / sqrt 3

3 ( 1/2 ) + 5 ( -sqrt 3 / 3 )

3 / 2 - 5 sqrt 3 / 3

( 9 - 10 sqrt 3 ) / 6