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)

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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)

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2 is a radius distance and cos = x and sin = y
a) (x = 2cos(60), y = 2sin(60))
How do you know that cos = x and sin = y?

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Other answers:

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

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