Question

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)

Answer 1

2 is a radius distance and cos = x and sin = y

Answer 2

a) (x = 2cos(60), y = 2sin(60))

Answer 3

How do you know that cos = x and sin = y?

Answer 4

And where'd the 60 come from?

Answer 5

this might help

Answer 6

Oh ok thanks. I have that in my notes and I already forgot what it was for. ugh

Answer 7

cos(t) is defined as x/r therefore x = r cos(t)

Answer 8

sin(t) = y/r ; y = r sin(t)

Answer 9

we can convert pi/3 into degrees by multiplying it by 180/pi

Answer 10

180pi/3pi = 60

Answer 11

right

Answer 12

so where does the (2, pi/3) come in?

Answer 13

cos(60) = 1/2 ; sin(60) = sqrt(3)/2

Answer 14

2cos(60) = 2(1/2) = 1 ; x = 1

2sin(60) = 2(sqrt(3)/2) = sqrt(3) ; y = sqrt(3)

Answer 15

why doesn't x = 2 and y = pi/3

Answer 16

those would be the rectanglular plots for the point.

otherwise, you just turn the required degrees and move out the required distance

Answer 17

since r = 2 and cos(60) = 1/2

2(1/2) = 1

Answer 18

pi/3 is an angle, not a point.

Answer 19

right.

Answer 20

you convert angles to a distance with the trig functions

Answer 21

polar coordinates can have many names for the same spot...

Answer 22

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

Answer 23

rutn is some stroke version of turn :)