Question

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°

Answer 1

the expression will be written like ("r value here", "angle here") pair

so to find what "r" or the modulus is, keep in mind that \(\bf r^2 = x^2 + y^2\)

to find the angle , well, use the trig identity of \(\bf tan(\theta) = \cfrac{y}{x}\implies tan^{-1}(tan(\theta)) = tan^{-1}\left(\cfrac{y}{x}\right)\implies \theta=tan^{-1}\left(\cfrac{y}{x}\right)\)

Answer 2

so would it plugged in as
=tan^-1(-4/4)?

Answer 3

you could do that... what... do inverse trigonometric functions give anyway?

Answer 4

No idea

Answer 5

try it in your calculator... what do you get for \(\bf tan^{-1}\left(\cfrac{4}{-4}\right)\)

Answer 6

well.... kinda got the negative in the wrong... .anyhow \(\bf tan^{-1}\left(\cfrac{-4}{4}\right)\)

Answer 7

-45!

Answer 8

or would it be positive?

Answer 9

ahh... -45? ducks? gremlins? racoons? degrees!

Answer 10

yes 45 degrees!

Answer 11

so inverse trig functions give an angle, so we... -45 will be in the 4th quadrant

Answer 12

since what you're asked is for 2 pairs.... so -45 is one.... \(\bf tan^{-1}\left(\cfrac{-4}{4}\right)=tan^{-1}(-1)\)

so the other angle will be the reference angle to that, where tangent is also -1.... which means the 2nd quadrant, why? because cosine is negative and sine is positive

Answer 13

so my answers on my sheet look like this.
(4 , radical 2, 45°), (-4 ,radical 2, 225°)

(4 ,radical 2, 135°), (-4 ,radical 2, 315°)

(4 ,radical 2, 225°), (-4 ,radical 2, 45°)

(4 ,radical 2, 315°), (-4 ,radical 2, 135°)

how do i find the other angle and how do i know which pair of parenthesis the answers go in

Answer 14

for polars keep in mind that "r" can be negative or positive, it has no consequence however on the magnitude of "r"