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convert
-4.51^i + 3.7^j to polar coordinates.
^ this is on top of the letters.
ok this is what i did...not sure if i am right or wrong
r^2 = 4.51^2 + 3.7^2 = 34.0301
r = sqrt34.0301
tan 0 = 4.51/3.7
and next i dont know
HELP
Desi
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You have the correct magnitude (r), but for the angle, use:
But keep in mind in which quadrant the point lies!
Also, are you supposed to express the result using the polar coordinate unit vectors?
Last edited by polylog (2006-10-05 05:28:20)
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yes with polar coordinates..
ok how to solve that...
put it in teh calculator
tan^-1 (3.7/-4.51)
tan3.7 divide by tan-4.51
rigght?
Desi
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The order of operations of something like this is *innermost operation first*, inside brackets.
So, we first divide, and then take the inverse tangent of the result:
(But remember in which quadrant the point is!)
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r = sqrt34.0301
small angle = -0.6871 right?
now we haev to measure countercloakwise and cloakwise from the positive x axis to get the polar angle
Desi
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Yes that's right.
To see what the polar angle is, it's best to draw a diagram with a line from (0, 0) to the original point (-4.51, 3.7), and you can see that you need to add pi/2 to 0.6871 to reach the point.
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Oops the angle should be (pi - 0.6871) = 2.45454
That's what I get for not drawing a diagram!
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but i still dont get it
Desi
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Look at the diagram (yeah I know its kindof ugly, lol):
We want the angle between the x-axis and the line from the origin (0, 0) to the point (-4.51, 3.7).
We have found that
by using the inverse tangent.
BUT, this is not the angle we want !!
The inverse tangent on the calculator gives you only the *smallest angle* which has a tangent of 3.7/-4.51.
This is because *many angles* can have the same tangent -- this is because the trig functions are periodic, that means their values repeat!
So, the calculator is not giving you exactly the angle you need, just an angle with the same tangent.
But this answer is very important anyway, since it lets us figure out what the actual angle is.
Looking at the diagram, we see that the angle we want will be pi/2 + something, which I've marked as "???".
We don't know what this is yet, but we do know that the angle from the negative x-axis to the line is 0.6871, because we know the angle on the other side, from the inverse tangent.
And we know that the unknown angle ("??") and 0.6871 must add to pi/2.
Therefore, this unknown angle is pi/2 - 0.6871
So we almost have the angle we want.. now we just have to see that the total angle from the x-axis all the way to the line to our point (-4.51, 3.7) is:
pi/2 + the unknown angle = pi/2 + (pi/2 - 0.6871) = pi - 0.6871 = 2.4545 (approximately)
All the measurements are in Radians of course.
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Thank you so veyr much for explaining and helping me out
now i kinda understood but still....
thanks
Desi
Raat Key Rani !
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