Question

Find the rectangular coordinates of the point with the polar coordinates (3, 5pi/3)

Answer 1

we know that :
\[x=r\cos \theta\\y=r\sin\theta\]
OK ?

Answer 2

Okay

Answer 3

3 = rcostheta
5pi/3 = rsintheta

Answer 4

you have :
\[r=3\\
\theta=\frac{5\pi}3
\]
Right ?

Answer 5

Idk, why is r 3? isnt x and y values 3 and 5pi/3 respectively?

Answer 6

x=0.5 and y=-2.598

Answer 7

by using abov given formulas

Answer 8

0.5 = 3cos(5pi/3)
-2.6 = 3sin(5pi/3)

Answer 9

@kjuchiha Listen to me carefully !
You are given the polar coordinates
The first of them is r
and the second is theta !

Get it ?

Answer 10

ohhh okay! cool

Answer 11

But now what?

Answer 12

x = 3cos(5pi/3)
y = 3sin(5pi/3)

Answer 13

cos 5pi/3 =0.5 now muplty 3*0.5 gives 0.5 so x=o.5
same as calculate y give -2.598

Answer 14

So much easier than it looks. Thanks fozia, I've got it now

Answer 15

@kjuchiha Yes

Answer 16

And you Noura! Almost forgot about you lol

Answer 17

You can find exact values :
\[x=r\cos\theta=3\cos\frac{5\pi}{3}=3\cos\left(\frac{5\pi}{3}-2\pi\right)=3\cos\frac{-\pi}{3}=3\times\frac12=\frac32\\
y=r\sin\theta=3\sin\frac{5\pi}{3}=3\sin\left(\frac{5\pi}{3}-2\pi\right)=3\sin\frac{-\pi}{3}=3\times\frac{-\sqrt3}2=-\frac{3\sqrt3}2\]

Answer 18

I see! That's kind of what i did after u told me x = rcostheta and y = rsintheta