Find the Exact Value cos(arcsin(0))

Problem

cos(arcsin(0))

Solution

1. Identify the inner function value by determining the angle θ such that sin(θ)=0 within the restricted range of the inverse sine function, which is [−π/2,π/2]

2. Evaluate the inverse sine expression:

arcsin(0)=0

3. Substitute the result back into the outer cosine function:

cos(0)

4. Determine the exact value of the cosine of 0 using the unit circle:

cos(0)=1

Final Answer

cos(arcsin(0))=1

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