Give the polar coordinate for each of the following rectangular coordinates

Question

(1,2) = (sqrt5,?)

(-24,13) = (27.295,?)

if you could work out the problems as well because im able to get the x coordinate, just not the y

Answer 1

(1,2) = (sqr5, 63.43 degrees)

use a calculator with an inverse trig function

find the inverse tangent of 2/1 = tan^-1(2) = about 63.43 degrees

if you draw a rought sketch, it looks about 60 degrees. Had it been (1, sqr3) = about (1, 1.732) it would have been exactly 60 degrees, so (1,2) is slightly more than 60 degrees

(-24, 13) is in quadrant II, so the angle will be somewhere between 90 and 180 degrees

find the inverse tangent of -13/24 = 151.56 degrees

for (x,y) = (r, A) the polar conversion equations are

x= rcosA,

y=rsinA,

tanA = y/x,

A = tan^-1(y/x)

x^2 + y^2 = r^2

r = sqr(x^2 + y^2)

for the 1st problem

r = sqr(1^2 +2^2)= sqr(1+4) = sqr5

A = tan^-1(2/1) = tan^-1(2) = about 63.43 degrees

for the 2nd problem

A = tan^-1(-13/24) = 151.56

If you're getting 28.44 or -28.44, that's a reference angle in quadrant I or an angle in quadrant IV. find it's counterpart in quadrant II. 180-28.44 = 151.56 Just by plotting the point, you know it's a quadrant III angle.

you can use a handheld calculator or an online calculator such as Desmos.