Solve x=3(cost sint)

Evaluate

x = 3 (cos (t) sin (t))

Simplify

More Steps

x = \frac{3 sin ( 2 t )}{2}

Interchange t and y

t = \frac{3 sin ( 2 y )}{2}

Swap the sides of the equation

\frac{3 sin ( 2 y )}{2} = t

Multiply both sides of the equation by \frac{2}{3}

\frac{3 sin ( 2 y )}{2} \times \frac{2}{3} = t \times \frac{2}{3}

Calculate

sin (2 y) = t \times \frac{2}{3}

Calculate

sin (2 y) = \frac{2}{3} t

Use the inverse trigonometric function

2 y = arcsin (\frac{2}{3} t)

Divide both sides

\frac{2 y}{2} = \frac{arcsin ( \frac{2}{3} t )}{2}

Divide the numbers

y = \frac{arcsin ( \frac{2}{3} t )}{2}

Solution

f^{- 1} (t) = \frac{arcsin ( \frac{2}{3} t )}{2}

Function