Find the cartesian coordinates of the point whose polar coordinates ar

1.	Find the cartesian coordinates of the point whose polar coordinates are 1 by 2 ,7 pi by 3
Answer» SOLUTION TO DETERMINE The cartesian coordinates of the point WHOSE polar coordinates are $\displaystyle \sf{ \bigg( \frac{1}{2} \: ,\: \frac{7\pi}{3} \bigg)}$ EVALUATION Let ( r , θ ) be the polar coordinates of a point and ( x, y) be the coordinates of the same point in Cartesian Coordinate system Then $\displaystyle \sf{r = \frac{1}{2} \: \: \: and \: \: \: \theta = \frac{7\pi}{3} }$ Now the relation between cartesian coordinate system and polar coordinate system is $\sf{x = r \cos \theta \: \: and \: \: y = r \sin \theta}$ $\displaystyle \sf{x = r \cos \theta}$ $\displaystyle \sf{ \implies \: x = \frac{1}{2} \cos \frac{7\pi}{3} }$ $\displaystyle \sf{ \implies \: x = \frac{1}{2} \times \frac{1}{2} }$ $\displaystyle \sf{ \implies \: x = \frac{1}{4} }$ Again $\displaystyle \sf{y = r \sin \theta}$ $\displaystyle \sf{ \implies \: y = \frac{1}{2} \sin \frac{7\pi}{3} }$ $\displaystyle \sf{ \implies \: y = \frac{1}{2} \times \frac{ \sqrt{3} }{2} }$ $\displaystyle \sf{ \implies \: y = \frac{ \sqrt{3} }{4} }$ Hence the REQUIRED cartesian coordinates $\displaystyle \sf{ \bigg( \: \frac{1}{4} \: ,\: \frac{ \sqrt{3} }{4} \: \bigg)}$ ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 1. Find the area of the region bounded by the curve y2 – 6y + x + 5 = 0 and y-axis. brainly.in/question/31154213 2. shortest distance from the origin to the PLANE x - 2y - 2z = 3 is brainly.in/question/30723676

Find the cartesian coordinates of the point whose polar coordinates are 1 by 2 ,7 pi by 3

Answer»

SOLUTION

TO DETERMINE

The cartesian coordinates of the point WHOSE polar coordinates are

$\displaystyle \sf{ \bigg( \frac{1}{2} \: ,\: \frac{7\pi}{3} \bigg)}$

EVALUATION

Let ( r , θ ) be the polar coordinates of a point and ( x, y) be the coordinates of the same point in Cartesian Coordinate system

Then

$\displaystyle \sf{r = \frac{1}{2} \: \: \: and \: \: \: \theta = \frac{7\pi}{3} }$

Now the relation between cartesian coordinate system and polar coordinate system is

$\sf{x = r \cos \theta \: \: and \: \: y = r \sin \theta}$

$\displaystyle \sf{x = r \cos \theta}$

$\displaystyle \sf{ \implies \: x = \frac{1}{2} \cos \frac{7\pi}{3} }$

$\displaystyle \sf{ \implies \: x = \frac{1}{2} \times \frac{1}{2} }$

$\displaystyle \sf{ \implies \: x = \frac{1}{4} }$

Again

$\displaystyle \sf{y = r \sin \theta}$

$\displaystyle \sf{ \implies \: y = \frac{1}{2} \sin \frac{7\pi}{3} }$

$\displaystyle \sf{ \implies \: y = \frac{1}{2} \times \frac{ \sqrt{3} }{2} }$

$\displaystyle \sf{ \implies \: y = \frac{ \sqrt{3} }{4} }$

Hence the REQUIRED cartesian coordinates

$\displaystyle \sf{ \bigg( \: \frac{1}{4} \: ,\: \frac{ \sqrt{3} }{4} \: \bigg)}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Find the area of the region bounded by the curve y2 – 6y + x + 5 = 0 and y-axis.

brainly.in/question/31154213

2. shortest distance from the origin to the PLANE x - 2y - 2z = 3 is

brainly.in/question/30723676