Solve for x 24arcsin(x)=4pi

Problem

24*arcsin(x)=4*π

Solution

1. Isolate the inverse sine function by dividing both sides of the equation by 24

24*arcsin(x)=4*π

arcsin(x)=(4*π)/24

2. Simplify the fraction on the right side by dividing the numerator and the denominator by their greatest common divisor, 4

arcsin(x)=π/6

3. Apply the sine function to both sides of the equation to solve for x noting that the sine is the inverse of the arcsine.

x=sin(π/6)

4. Evaluate the sine of π/6 using the unit circle or special right triangles.

x=1/2

Final Answer

x=1/2

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