Let $P$ be any point and let $OP=r$, where $O$ is the origin and let $OP$ make an angle $\theta$ with the axis, then $r$ and $\theta$ are called Polar coordinates of the point $P$, and the coordinates may be written as $(r,\theta)$.

Find the Cartesian equations of

(b) $r\cos(\theta-\alpha)=p$

RELATIONSHIPS BETWEEN

chegendungu

$\cos(\theta-\alpha)=p$

$\cos(\theta-\alpha)$ may be expanded

$\therefore r\cos\theta\cos\alpha+r\sin\theta\sin\alpha=p$

Therefore the Cartesian equation of $r\cos(\theta-\alpha)=p$ is

$x\cos\alpha+y\sin\alpha=p$

$Note$. The perpendicular from the origin to this line is of length $p$ and makes an angle $\alpha$ with the x-axis. This form of equation of a straight line is known as the normal or perpendicular form.

Surround your text in `*italics*`

or `**bold**`

, to write a math equation use, for example, `$x^2+2x+1=0$`

or `$$\beta^2-1=0$$`

Stats

Views: 11

Asked: 2 years ago