Polar Coordinates Points

[greatwhiteshark]

Plot each point given in polar coordinates and find other polar coordinates (r, theta) of the point for which a) r > 0, -2PI < or = to theta < 0
and b) r < 0, 0 < or = to theta < 2PI and c) r > 0, 2PI < or = to theta < 4PI.

1) (5, 2PI/3)

2) (1, PI/2)

 

[soroban]

Hello, Janet!

That funny symbol π is "pi".

I'll walk through the first one . . .

Plot each point given in polar coordinates
and find other polar coordinates (r, θ) of the point for which:

a) / r > 0, . -2π <u><</u> θ < 0 . . positive r, but negative θ

b) .r < 0, .0 <u><</u> θ < 2π . . positive θ, but negative r

c) .r > 0, .2π <u><</u>θ < 4π . . positive r, but θ is between 360° and 720°

1) . (5, 2π/3)

1) . (5, 2π/3) .is in quadrant 2.
It has radius 5 and makes a 120° angle with the positive x-axis.

a) .For a negative angle, use -240° = -4π/3
. . . Answer: .(5,-4π/3)

b) .For a negative r, we go around to 300° = 5π/3 and "back up" 5 units.
. . . Answer: .(-5, 5π/3)

c) .For an angle between 2π and 4π, add 2π to our θ.
. . . . . The angle is: .2π/3 + 2π .= .8π/3
. . . Answer: .(5, 8π/3)

 

[greatwhiteshark]

Soroban

Soroban,

Like always, great work! I don't understand why our teacher loves to write questions on the board that he has not covered in class. This is not good teaching at all. Your view?