Question

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.(5. - %)

Answer 1

we have the point

(5, -pi/6)

where

r=5

θ=-pi/6

see the figure below to better understand the problem

The given point lies in the IV quadrant

so

the x-coordinate is positive

the y-coordinate is negative

Remember that

x=rcosθ

y=rsinθ

so

x=5*cos(pi/6)=(5√3)/2

y=5*sin(pi/6)=-5/2

therefore

the coordinates are

((5√3)/2,-5/2)