Question

Aisha used a compass to walk 59° south of west for 3.50 miles, then stopped for lunch. Assume that the point from which she started her hike corresponds to the origin of the coordinate system.

(a) Find the polar coordinates corresponding to the place where Aisha stopped for lunch. (Enter your answer for r in miles and counterclockwise from the +x-axis. Round your answers to at least th ree significant figures. as the smallest positive angle in degrees r =26
The radial polar coordinate does not coincide with x. mi =
(b) Find the Cartesian coordinates (in miles) for the same point.
x = 2.6
Use the relations between polar and Cartesian coordinates to find the coordinate x. mi
y = 4.24
Use the relations between polar and Cartesian coordinates to find the coordinate y. mi

Answer 1

Step-by-step explanation:

a )

59° south of west means (180 + 59 )° counterclockwise from the +x-axis.

so angle θ = 239 ° .

r = 3.5 miles .

polar coordinates ( r , θ )

= ( 3.50 , 239° )

As the smallest positive angle in degree is 26 then 26 x 9 = 234

so rounding off 239 to 234 , the angle will be 234

polar coordinates ( 3.50 , 234 )

b )

Cartesian coordinates (in miles) for the same point

x coordinate = r cosθ = 3.5 cos 234 = - 2.06 mi

y coordinate = r sinθ = 3.5 sin 234 = - 2.83 mi