Bit of a problem with polar coordinates.

In summary, the problem involves finding the rectangular coordinates of a point given its polar coordinates. The formulas used are x = r cos Theta and y = r sin Theta. The given polar coordinate point is (rad2, 4.39) and the values of r and Theta are substituted into the formulas. However, the calculated values of x and y do not match the given answers. It is suggested to check if the calculator is in radian mode and if not, convert the value of 4.39 into degrees by multiplying it by 180/pi. This will give the correct answers of x = -0.45 and y = -1.34.
  • #1
kryptos
5
0
Bit of a problem with polar coordinates. (Only trig knowledge needed.)

Right. So, in this problem, I'm given the polar coordinate point (rad2, 4.39) -- "rad2" being, naturally, short for radical 2. I'm to find the rectangular coordinates of the point, using the formulas:

x = r cos Theta

and y = r sin Theta. In this problem, r = rad2 and Theta = 4.39.

Simple, no? Only for some reason, it's not coming out right with my calculator. I substitute the givens, for:

x = rad2 * (cos 4.39)

and y = rad2 * (sin 4.39).

I have the answers -- they're in the back of the textbook -- but can't figure out the process. x should equal approx. -0.45, and y should equal -1.34. Instead, I find x to equal 1.41 and y to equal 0.11. Am I doing something in the wrong order?

Any help is appreciated. Thanks. ; )
 
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  • #2
Are you sure your calculator is in radian mode and not degree mode if the 4.39 is inradians?
 
  • #3
Actually, no. I hadn't thought of that. But I don't know how to set it in radian mode. Is there some way I could convert the 4.39 into a form usable in degree mode?
 
  • #4
kryptos said:
Actually, no. I hadn't thought of that. But I don't know how to set it in radian mode. Is there some way I could convert the 4.39 into a form usable in degree mode?

Multiply by 180/pi.
 
  • #5
d_leet said:
Multiply by 180/pi.

. . . . . . . .

*smacks forehead*

I can't believe I missed that. Thanks so much.
 

1. What are polar coordinates and how are they different from Cartesian coordinates?

Polar coordinates are a system of locating points in a two-dimensional plane using a distance from the origin and an angle from a reference line. This is different from Cartesian coordinates, which use two perpendicular axes (x and y) to locate points.

2. What is the main advantage of using polar coordinates over Cartesian coordinates?

The main advantage of polar coordinates is that they are more suitable for representing and working with circular or curved shapes. This is because the distance and angle measurements are more natural for these types of shapes.

3. How do you convert between polar and Cartesian coordinates?

To convert from polar coordinates (r, θ) to Cartesian coordinates (x, y), use the formulas x = r cos(θ) and y = r sin(θ). To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), use the formulas r = sqrt(x^2 + y^2) and θ = arctan(y/x).

4. Can you use polar coordinates in three-dimensional space?

No, polar coordinates are only applicable in two-dimensional space. In three-dimensional space, a system of spherical coordinates is used, which incorporates a distance from the origin, an angle from a reference plane, and an angle from a reference line.

5. How are polar coordinates used in science and engineering?

Polar coordinates are commonly used in fields such as physics, engineering, and astronomy to represent and analyze circular or rotational motion, as well as in the design of circular or cylindrical objects. They are also used in mapping and navigation, particularly in polar regions.

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