What are the components of the vector between the origin and the polar coordinate (10, (7pi)/6)(10,7π6)?

1 Answer
Feb 19, 2016

Components are -5sqrt353 along xx axis and -55 along yy axis.

Explanation:

Components of a vector between the origin and the polar coordinate (r,theta)(r,θ) can be written as (rcostheta, rsintheta)(rcosθ,rsinθ), where rcosthetarcosθ is the component along xx axis and rsinthetarsinθ is the component along yy axis.

Hence, components of a vector between the origin and the polar coordinate (10,(7pi)/6)(10,7π6) are

10cos(7pi/6)10cos(7π6) or 10*(-cospi/6)10(cosπ6) i.e. 10*-sqrt3/21032

or -5sqrt353 along xx axis

10sin(7pi)/610sin(7π)6 or 10*(-sinpi/6)10(sinπ6) i.e. 10*-1/21012

or -55 along yy axis