For the given point in polar coordinates, how do you find the corresponding rectangular coordinates for the point. (4, -pi/2)?

Question

For the given point in polar coordinates, how do you find the corresponding rectangular coordinates for the point.  (4, -pi/2)?

Carter Anderson · Accepted Answer

#(4,-pi/2)to(0,-4)# To convert from #color(blue)"polar to rectangular coordinates"# #color(orange)"Reminder"# #color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))# here r = 4 and #theta=-pi/2# #rArrx=4cos(-pi/2)=4xx0=0# and #y=4sin(-pi/2)=4xx-1=-4# #rArr(4,-pi/2)to(0,-4)#

Abigail Armstrong · Answer

undefined To find the corresponding rectangular coordinates for the point $ (4, -\frac{\pi}{2}) $ given in polar coordinates:

$$ x = r \cdot \cos(\theta) $$
$$ y = r \cdot \sin(\theta) $$

where $ r $ is the radius and $ \theta $ is the angle in radians.

Substitute $ r = 4 $ and $ \theta = -\frac{\pi}{2} $ into the formulas:

$$ x = 4 \cdot \cos\left(-\frac{\pi}{2}\right) $$
$$ y = 4 \cdot \sin\left(-\frac{\pi}{2}\right) $$

Evaluate the trigonometric functions:

$$ x = 4 \cdot 0 $$
$$ y = 4 \cdot (-1) $$

$$ x = 0 $$
$$ y = -4 $$

So, the corresponding rectangular coordinates are $ (0, -4) $.