Posted by Cindy on Thursday, December 15, 2011 at 12:29pm.
There are two common ways to describe a point in the plane.
Most familiar is the rectangular coordinates (x,y) which says how far left-right or up-down the point is from the origin (0,0).
Another way is to specify how far away a point is from the pole (0,0), and in which direction θ. The direction is usually expressed as 0-360° when first learning about polar coordinates.
So, you need to get familiar with the circle and how to handle degrees.
An (x,y) pair can be determined from an (r,θ) pair by referring to the right triangle with the vector to the point as hypotenuse.
x = r cosθ
y = r sinθ
to go the other way,
tanθ = y/x
r2 = x2 + y2
If all this looks unfamiliar, you need to check your textbook and have a one-on-one session with someone in person.
It sounds like your question is referring to a point where
θ = 41°
r = 77
To get the (x,y) coordinates,
x = 77 cos 41° = 58.1
y = 77 sin 41° = 50.5
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