Find the cartesian coordinates
If (x,y) = (-3,8) then (r,theta) = ?
I already got r it is -sqrt73 but i cant seem to get theta right.
I got 110.556 but its wrong...please tell me how to do it thank you!!
x = - 3 , y = 8
QUADRANT II
arc tan ( sqrt 73 ) = 83.324408°
tan ( theta ) = - sqrt ( 73 )
theta = 180 ° - 83.324408°
theta = 96.675592°
theta = 96° 40' 32"
I don't agree with the above Ø
r = √(x^2+y^2)= √73
angle in standard position = arctan(8/3) = 69.44°
since (-3,8) is in II
Ø = 180-69.44 = 110.56°
(-3,8) ----> (√73, 110.56°)
Both of these answers are still wrong
To find the polar coordinates (r,θ) given the cartesian coordinates (x,y), you can use the following formulas:
r = √(x^2 + y^2)
θ = atan2(y, x)
Let's calculate θ step by step using the given cartesian coordinates (-3,8):
1. Calculate the value of atan2(y, x):
θ = atan2(8, -3)
2. Use a calculator to evaluate atan2(8, -3):
θ ≈ 109.471
Therefore, the polar coordinates (r,θ) corresponding to the cartesian coordinates (-3,8) are approximately (−√73, 109.471). Note that the angle is measured in degrees.