The polar coordinates of a point are given Find the rectangu

The polar coordinates of a point are given. Find the rectangular coordinates of this point. What are the rectangular coordinates of this point? (Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

( 5 , pi/6 )

r = 5

theta = pi/6 = 30 deg

x = r cos theta = 5 cos 30 = 5 ( sqrt 3/2 ) = 5 sqrt 3 / 2

y = r sin theta = 5 sin 30 = 5 ( 1/2) = 5/2

rectangular coordinates are

( 5 sqrt 3 / 2 , 5/2 )