Find the exact value:

Question

1.) cos^-1(sin(pi/2))

2.) arccos(cos(7pi/2))

Answer 1

1. cos^-1(sin(π/2)
we know sin π/2 = 1
so cos^-1 (sin π/2)
= cos^-1 (1)
= 0

(because cos 0 = 1 )

2. this one is easy, since arccos is the same as cos^-1
the answer is obviously 7π/2
However, they might just want a reduced answer
since cos 7π/2 = cos 3π/2
arccos(cos(7π/2) )
= arccos(cos (3π/2))
=3π/2