Question

Q7 Q16.) Convert the polar equation to a rectangular equation.

Answer 1

In polar coordinates, we have


`x=r\cos\theta\implies\cos\theta=\frac xr`

`y=r\sin\theta\implies\sin\theta=\frac yr`

From this we can write


`\tan\theta=(\sin\theta)/(\cos\theta)=(\frac yr)/(\frac xr)=\frac yx`

If
`\theta=\frac{4\pi}3`, then
`\tan\theta=\sqrt`, so we get


`\frac yx=\sqrt3\implies y=\sqrt3\,x`