How do you convert $(7, \frac{5 π}{6})$ $(7, (5pi)/6)$ into cartesian form?

Question

4660 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-11T17:34:43

The cartesian form is $(- \frac{7}{2} \sqrt{3}, \frac{7}{2})$ $(-7/2sqrt3, 7/2)$

To convert from polar coordinates $(r, θ)$ $(r,theta)$ to cartesian coordinates $(x, y)$ $(x,y)$ , we use the following equations

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

Therefore,

$x = 7 cos (\frac{5}{6} π) = - 7 \cdot \frac{\sqrt{3}}{2} = - \frac{7}{2} \sqrt{3}$ $x=7cos(5/6pi)=-7*sqrt3/2=-7/2sqrt3$

$y = 7 sin (\frac{5}{6} π) = 7 \cdot \frac{1}{2} = \frac{7}{2}$ $y=7sin(5/6pi)=7*1/2=7/2$

How do you convert (7, (5pi)/6)(7,5π6)(7, (5pi)/6) into cartesian form?