Find the exact value of the composition function without using a calculator: 1. tan-1(sin pi/2) 2. tan(2cos-1 (1/2))

composition-function

#1

Find the exact value of the composition function without using a calculator:
1. tan-1(sin pi/2) 2. tan(2cos-1 (1/2))

Answer:

  1. sin(pi/2) = 1
    arctan(sin (pi/2)) = arctan1 = pi/4

  2. arccos (1/2) = pi/3
    tan( 2arccos (1/2)) = tan (2pi/3) = tan(pi/2 + 30) = -cot30 = -sqrt3