If the cartesian coordinates of a point are given by (2, y)
and its polar coordinates are (r, 30°), determine y and r.
4. Two points in a plane have polar coordinates (2.50 m,
30.0°) and (3.80 m, 120.0°). Determine (a) the cartesian
coordinates of these points and (b) the distance
between them.

Question

If the cartesian coordinates of a point are given by (2, y)
and its polar coordinates are (r, 30°), determine y and r.
4. Two points in a plane have polar coordinates (2.50 m,
30.0°) and (3.80 m, 120.0°). Determine (a) the cartesian
coordinates of these points and (b) the distance
between them.

parthkohli · Answer

You know that the rectangular coordinates for polar coordinates $(r,\theta)$ are given by $(r\cos\theta, r\sin\theta)$.

parthkohli · Answer

Use that fact, maybe?

marco26 · Answer

x=rcos(theta)   , y=rsin(theta)

parthkohli · Answer

$$r\cos30^{\circ} = 2$$What is $\cos(30^{\circ})$?

goformit100 · Answer

root 3 by 2

parthkohli · Answer

Correct.$$r \times \dfrac{\sqrt{3}}{2} = 2$$Find $r$.

goformit100 · Answer

4 by root 3

parthkohli · Answer

Nice! Can you find $y$ now? It's $r\sin(30^{\circ}) = \dfrac{4}{\sqrt3} \times 0.5$

goformit100 · Answer

Thankyou Sir

parthkohli · Answer

Koi nahi re! X-D