Question

Change (-5, -7) into polar form. Round both r and θ to the nearest tenth.
Help plz??

Answer 1

this is how i did it..but i'm not sure

Answer 2

x = -5 y = -7

r = sqrt(x^2 + y^2) = sqrt
r = sqrt(x^2 + y^2) = sqrt(74) = 8.60
theta = tan^1 (y/x) = tan^1 (5/7) = 35.5 degrees.

The polar coordinates are approximately (8.6, 35.5 degrees)

Answer 3

Given the rectangular coordinates, (x, y),
To get the polar coordinates (r, θ), use these formulas
\[r = \sqrt{x^{2} + y^{2}}\]
and (I'm assuming you have a calculator at your disposal)
\[\theta=\tan^{-1}\left| \frac{y}{x} \right|\]if BOTH x and y are positive\[\theta=180°-\tan^{-1}\left| \frac{y}{x} \right|\]if x is negative and y is positive\[\theta=180°+\tan^{-1}\left| \frac{y}{x} \right|\]if BOTH x and y are negative and finally\[\theta=360°-\tan^{-1}\left| \frac{y}{x} \right|\]if x is positive and y is negative

Answer 4

You seem to have gotten r down well enough, but remember, given that both x and y are negative, and your angle is less than 90 degrees, that means your coordinates are in the FIRST quadrant, is that really the case?

Answer 5

ohhh ok

Answer 6

See, both x and y are negative, and your calculator only displays values from 0 to 90 for inverse trigs (I think?)
So better use that third formula for theta to ensure that it ends up in the third quadrant as it should :)

Answer 7

ok thanks

Answer 8

so i'll use theta = 180 degrees - tan one or?

Answer 9

anybody??