What is the inverse of f(x)=sqrt(2/pi)*sin(r) ?

The inverse of f(x)=sqrt(2/pi)*sin(r) is arcsin((sqrt(2)sqrt(pi)r)/2)

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inverse of f(x)=sqrt(2/pi)*sin(r)

inverse

f (x) = \frac{2}{π} \cdot sin (r)

arcsin (\frac{2 π r}{2})

Solution steps

Solve for

sin (r), x = \frac{2}{π} \cdot sin (r)

sin (r) = \frac{2 π x}{2}

sin (a) = b \Rightarrow a = arcsin (b)

arcsin (\frac{2 π x}{2})

Substitute

x = r

arcsin (\frac{2 π r}{2})

What is the inverse of f(x)=sqrt(2/pi)*sin(r) ?
The inverse of f(x)=sqrt(2/pi)*sin(r) is arcsin((sqrt(2)sqrt(pi)r)/2)