What is the inverse of f(x)=4cos(pix+pi/2) ?

The inverse of f(x)=4cos(pix+pi/2) is (2arccos(x/4)-pi)/(2pi)

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inverse of f(x)=4cos(pix+pi/2)

inverse

f (x) = 4 cos (π x + \frac{π}{2})

\frac{2 arccos ( \frac{x}{4} ) - π}{2 π}

Solution steps

Solve for

cos (π x + \frac{π}{2}), y = 4 cos (π x + \frac{π}{2})

cos (π x + \frac{π}{2}) = \frac{y}{4}

cos (a) = b \Rightarrow a = arccos (b)

π x + \frac{π}{2} = arccos (\frac{y}{4})

Solve for

x, π x + \frac{π}{2} = arccos (\frac{y}{4})

\frac{2 arccos ( \frac{y}{4} ) - π}{2 π}

Substitute

y = x

\frac{2 arccos ( \frac{x}{4} ) - π}{2 π}

What is the inverse of f(x)=4cos(pix+pi/2) ?
The inverse of f(x)=4cos(pix+pi/2) is (2arccos(x/4)-pi)/(2pi)