Simplify cos(arcsin(( square root of 3)/2))

Problem

cos(arcsin(√(,3)/2))

Solution

1. Evaluate the inner inverse trigonometric function arcsin(√(,3)/2) by finding the angle θ in the interval [−π/2,π/2] such that sin(θ)=√(,3)/2

θ=π/3

2. Substitute the value of the angle back into the outer trigonometric function.

cos(π/3)

3. Calculate the cosine of the resulting angle using the unit circle or special right triangles.

cos(π/3)=1/2

Final Answer

cos(arcsin(√(,3)/2))=1/2

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