Question

Can you help me find the rectangular coordinates of each point
(5,pi/4)
(-2,pi/6)
(-1,2pi/3)

Answer 1

I'm assuming each point is in polar form (r,theta)

Answer 2

Yes they are

Answer 3

You can use these formulas

x = r*cos(theta)
y = r*sin(theta)

make sure you are in radian mode

Answer 4

so 5*cos(theta) and pi/4*sin(theta)

Answer 5

(r,theta) = (5,pi/4)

so

r = 5
theta = pi/4

Answer 6

x = r*cos(theta) = 5*cos(pi/4) = ??

y = r*sin(theta) = 5*sin(pi/4) = ??

Answer 7

(3.54, 3.54)

Answer 8

\(\large \begin{array}{cccllll}
5&,&(\frac{\pi}{4})\\
r&&\theta
\end{array}\qquad
\begin{cases}
x=rcos(\theta)\\
y=rsin(\theta)
\end{cases}\qquad
\begin{array}{cccllll}
x&,& y\\
\uparrow &&\uparrow \\
rcos(\theta)&&rsin(\theta)
\end{array}\)

Answer 9

since \[\Large \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\] and \[\Large \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\]

this means \[\Large (x,y) = \left(\frac{5\sqrt{2}}{2},\frac{5\sqrt{2}}{2}\right)\]

Answer 10

that is the exact form, but the approximate form works as well

Answer 11

ok thanks!

Answer 12

np