Question

Convert (5, pi/4) to rectangular coordinates.

Answer 1

Answer:

Rectangular Coordinates:

$x=\frac{5\sqrt{2}}{2}$

$y=\frac{5\sqrt{2}}{2}$

Step-by-step explanation:

Polar coordinate are given in the form:

$(r,\theta)$

The point given is:  $(5, \frac{\pi}{4})$

So,

$r=5$

and

$\theta=\frac{\pi}{4}$

The formula to convert polar coordinates to rectangular coordinates (x, y) is:

$x=rCos \theta$

$y=rSin\theta$

Note that  $sin(\frac{\pi}{4})=cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$

Thus,

$x=rCos\theta=5Cos(\frac{\pi}{4})=5*\frac{\sqrt{2}}{2}=\frac{5\sqrt{2}}{2}$

$y=rSin\theta=5*Sin(\frac{\pi}{4})=5*\frac{\sqrt{2}}{2}=\frac{5\sqrt{2}}{2}$