Exact Value

Question

(A)

 

Cos( cos^-1 4/5)

 

(B)

 

sin^-1 (sin 3pie/2)

Answer 1

Cos and cos^-1 are inverses of one another, so cos(cos^-1(4/5)) = 4/5

 

Same for sin and sin^-1.

 

(BTW, it's "pi" not "pie")

Answer 2

(B). sin^-1(sin(3π/2)) = sin^-1(-1) = -π/2

 

     (the range of the inverse sine is [-π/2,π/2])

 

     sin^-1(sinθ) = θ only when θ is in the interval [-π/2, π/2]

 

(A). cos(cos^-1x) = x for any x in the interval [-1,1]

 

      So, cos(cos^-1(4/5)) = 4/5