## anonymous one year ago Polar coordinates of a point are given. Find the rectangular coordinates of the point. (-5, -180°) a. (-5,0) b. (0,-5) c. (0,5) d. (5,0)

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1. anonymous

@freckles

2. SolomonZelman

$$y=r\cdot \sin(\theta)$$ $$x=r\cdot \cos(\theta)$$

3. SolomonZelman

You are given that: $$r=-5$$ $$\theta = -180^\circ$$

4. anonymous

So, -5x-180?

5. anonymous

Sorry, I am teaching myself. I am somewhat confused. I need help.

6. SolomonZelman

This is in general: $$y=r\cdot \sin(\theta)$$ $$x=r\cdot \cos(\theta)$$ (if you want to know why these values are what x and y are equivalent to, then let me know) And in our case, $$y=(-5)\cdot \sin(-180)=(-5)\cdot 0=0$$ $$x=(-5)\cdot \cos(-180)=(-5)\cdot(-1)=5$$

7. anonymous

Oh okay. I see now.

8. anonymous

I am writing this down.

9. SolomonZelman

|dw:1444238217960:dw|

10. SolomonZelman

The length of the base is x, and the length of the side is y. This is (roughly) how cartesian coordinates are represented (ok?)

11. anonymous

I am still here. I am writing this down.

12. SolomonZelman

And polar coordinates are represented differently: You face the direction of $$\huge _{^\theta}$$ and you walk in this direction $$\huge _{^{_r}}$$ units long.

13. SolomonZelman

14. SolomonZelman

as it is now I will assume you got no questions.

15. anonymous

I am understanding well.

16. SolomonZelman

And based on the diagram 9above), you can see that: $$\sin(\theta)={\rm opposite/hypotenuse}=y/r$$ $$\cos(\theta)={\rm adjacent/hypotenuse}=x/r$$ (this is simple trigonometry) Now, multiply both sides of each equation times r. You will get: $$\displaystyle \color{red}{ r \times}\sin(\theta)=\color{red}{ r \times}\frac{y}{r}$$ $$\displaystyle\color{red}{ r \times}\cos(\theta)=\color{red}{ r \times}\frac{x}{r}$$ (r cancels on the right side of each of the equations) $$\displaystyle r\sin(\theta)=y$$ $$\displaystyle r\cos(\theta)=x$$

17. SolomonZelman

Thus, knowing the angle, you can convert any polar coordinate to cartesian coordinate (just as we did in the example  (-5, -180°) )

18. anonymous

Okay, I see.

19. SolomonZelman

I mean: knowing the angle and the radius.

20. SolomonZelman

Are you doing calculus with polar coordinates, or this is some other course?

21. anonymous

Pre-Calculus.

22. SolomonZelman

Oh, cool. You will encounter it more in calculus, but as it is right now, good luck!

23. SolomonZelman

And if anything there are many people who are willing to help with stuff.....

24. SolomonZelman

bye