Solve for x 15arcsin(x)=5pi

Problem

15*arcsin(x)=5*π

Solution

1. Isolate the inverse sine function by dividing both sides of the equation by 15

15*arcsin(x)=5*π

arcsin(x)=(5*π)/15

2. Simplify the fraction on the right side of the equation.

arcsin(x)=π/3

3. Apply the sine function to both sides to solve for x

sin(arcsin(x))=sin(π/3)

x=sin(π/3)

4. Evaluate the sine of π/3 using the unit circle or special triangles.

x=√(,3)/2

Final Answer

x=√(,3)/2

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