Convert polar form to rectangular form and vise versa.

[jbjaidee]

Convert polar form to rectangular form:

50/-40=

Convert rectangular form to polar form:

15-j20=

If anyone can help that would be great, I haven't done this kind of math in a long time. Step by step so I can understand how to solve please. Thanks!

 

[Dr.Peterson]

Convert polar form to rectangular form:

50/-40=

Convert rectangular form to polar form:

15-j20=

If anyone can help that would be great, I haven't done this kind of math in a long time. Step by step so I can understand how to solve please. Thanks!

As I mentioned on your other question, it took me a bit to realize what you are asking here, as you didn't give the background you did there. Again, your 50/-40 is meant to be phasor form, namely 50∠-40°, meaning magnitude 50, angle -40°, for anyone who is reading this and has no idea what you are saying!

The page I referred to there contains both conversions. Here's the work for the first:

x = r cosθ = 50 cos(-40°) = 38.3
y = r sinθ = 50 sin(-40°) = -32.1
​

(Use whatever precision is appropriate).

For the second, use the conversion I described before:

r = √(x² + y²) = √(15² + (-20)²) = √625 = 25
θ = tan^-1(y/x) = tan^-1(-20/15) = -53.1°;
​

since x is positive and y is negative, we are in the fourth quadrant, and this angle is appropriate. If we were in the second quadrant, we would add 180°.

If you need help using your calculator, or with any other detail, let us know.

 

[jbjaidee]

Thank you so much for the help! I'm sorry, I didn't explain the second post that well. I didn't think the first one had gone through for some reason. Or I explained to much and confused people.

If you could give me some direction on how to solve the problem on my calculator that would be great! I have a simple TI-30X IIS. I assume I get to use the SIN, COS, and TAN buttons. Thanks

 

[Dr.Peterson]

Thank you so much for the help! I'm sorry, I didn't explain the second post that well. I didn't think the first one had gone through for some reason. Or I explained to much and confused people.

If you could give me some direction on how to solve the problem on my calculator that would be great! I have a simple TI-30X IIS. I assume I get to use the SIN, COS, and TAN buttons. Thanks

The first post was delayed so a moderator could approve it; that should have been mentioned when you registered. A lot of people seem to miss it. This message was likewise delayed; after the first three or so, you should get straight in. This helps prevent spam or worse.

I have the same calculator here, which makes it easy. (It's the one I recommend to students.)

Here's the work for the first, with keystrokes:

x = r cosθ = 50 cos(-40°) = 38.3 -- Enter 50 COS (-) 40 ) =
y = r sinθ = 50 sin(-40°) = -32.1 -- Enter 50 SIN (-) 40 ) =
​

Make sure the display says "DEG" in the lower right; if not, then you have to get it back to the default by pressing DRG and left or right arrow keys, then =.

Note that a negative sign is on a button labeled "(-)", not the subtract button, "-".

When you press SIN or COS, the display will also show "("; that's why you have to enter a ")" at the end to match it (though really, the calculator will pretend it's there if you forget; this is just a good habit). At the end, the calculator display will show essentially what I showed for the formula, but without the degree sign.

Here's the second:

r = √(x² + y²) = √(15² + (-20)²) = √625 = 25 -- Enter √ 15 ^ 2 + ( (-) 20 ) ^ 2 ) =
θ = tan^-1(y/x) = tan^-1(-20/15) = -53.1° -- Enter 2nd TAN (-) 20 ÷ 15 ) =
​

Here, you get √ by "2nd" followed by the key labeled x², which shows √ above it. When you do, it will put a "(" after the symbol, as it did with sin and cos, to make sure that everything following the radical is "inside" the radical, until you close it with ")". The display will show what I wrote for the formula but with ^ marking the two exponents.

Similarly, 2nd TAN will display "tan^-1(", including the parenthesis.

I hope that makes everything clear. You can read your calculator manual (or find it online) to make sure you understand the underlying basics.

 

[mmm4444bot]

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