anonymous
  • anonymous
Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r>0 and one with r<0 A. (2,pi/3) B. (1,-3pi/4) C. (-1, pi/2)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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amistre64
  • amistre64
2 is a radius distance and cos = x and sin = y
amistre64
  • amistre64
a) (x = 2cos(60), y = 2sin(60))
anonymous
  • anonymous
How do you know that cos = x and sin = y?

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anonymous
  • anonymous
And where'd the 60 come from?
amistre64
  • amistre64
this might help
1 Attachment
anonymous
  • anonymous
Oh ok thanks. I have that in my notes and I already forgot what it was for. ugh
amistre64
  • amistre64
cos(t) is defined as x/r therefore x = r cos(t)
amistre64
  • amistre64
sin(t) = y/r ; y = r sin(t)
amistre64
  • amistre64
we can convert pi/3 into degrees by multiplying it by 180/pi
amistre64
  • amistre64
180pi/3pi = 60
anonymous
  • anonymous
right
anonymous
  • anonymous
so where does the (2, pi/3) come in?
amistre64
  • amistre64
cos(60) = 1/2 ; sin(60) = sqrt(3)/2
amistre64
  • amistre64
2cos(60) = 2(1/2) = 1 ; x = 1 2sin(60) = 2(sqrt(3)/2) = sqrt(3) ; y = sqrt(3)
anonymous
  • anonymous
why doesn't x = 2 and y = pi/3
amistre64
  • amistre64
those would be the rectanglular plots for the point. otherwise, you just turn the required degrees and move out the required distance
amistre64
  • amistre64
since r = 2 and cos(60) = 1/2 2(1/2) = 1
amistre64
  • amistre64
pi/3 is an angle, not a point.
anonymous
  • anonymous
right.
amistre64
  • amistre64
you convert angles to a distance with the trig functions
amistre64
  • amistre64
polar coordinates can have many names for the same spot...
amistre64
  • amistre64
you can turn the required degrees, or turn in the opposite direction till you get to the spot, you can rutn 180 degrees less and just walk backwards to get there...etc
amistre64
  • amistre64
rutn is some stroke version of turn :)

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