a Find the exact value of arccossin 3pi2 b Find the exact va

(a) Find the exact value of arccos(sin 3pi/2)

(b) Find the exact value of arcsin(sin 2pi/3)

Solution

a) given arccos(sin 3pi/2)

use sinx = cos(pi/2 - x)

  arccos(sin 3pi/2) = arccos(cos (pi/2 -3pi/2))

= arccos(cos(-pi))

= pi (3.14159 decimal

b) arcsin(sin 2pi/3)

use sin2x = 2sinx cosx

arcsin(sin 2pi/3) = arcsin(2 sinpi/3 cospi/3 )

= arcsin(2 sinpi/3 1/2)

= arcsin(sinpi/3)

=pi/3 [ 1.04720 in decimals