Compare the graph of sin(arcsin(x)) and arcsin(sin(x)). Name he domains and ranges of each graph.?

Answer 1

1)
y = sin(arcsin(x)) = x
Domain: (-1, 1)
Range: (-1, 1)

2)
y = arcsin(sin(x))
Domain: (-∞, ∞)
Range: (-π/2, π/2)

a)
y = arcsin(sin(x)) = x
for
-π/2 ≤ x ≤ π/2

b)
y = arcsin(sin(x)) = -x + π
for
π/2 ≤ x ≤ 3π/2

c)
y = arcsin(sin(x))
is a periodic function in the whole domain (-∞, ∞) with period 2π

Such zig-zag pattern is because function arcussinus has a range of angles -π/2 to π/2 only.

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