Question

Given f (x) = sin x and g (x) = cos x, show that f (g (⅖)) = O. Show all your
steps.

Answer 1

Do you mean the input x = 2/5 (0.4) or x = π/2? Your text "⅖" reads as 2/5, but the only simple exact-zero value for this composition is at x = π/2. I'll give both possibilities.

1) If x = π/2:
- g(π/2) = cos(π/2) = 0.
- f(g(π/2)) = f(0) = sin(0) = 0.
So f(g(π/2)) = 0.

2) If x = 2/5:
- g(2/5) = cos(2/5) ≈ cos(0.4) ≈ 0.92106.
- f(g(2/5)) = sin(cos(2/5)) ≈ sin(0.92106) ≈ 0.79747.
So f(g(2/5)) ≈ 0.79747, which is not 0.

Tell me which input you intended if you want a specific worked solution.