What are the components of the vector between the origin and the polar coordinate (9, (-3pi)/4)?

1 Answer
Jim G.
Mar 16, 2016

((-9/2sqrt2),(-9/2sqrt2))

Explanation:

Using the formulae that link Polar to Cartesian coordinates.

• x = rcostheta

• y = rsintheta

here r = 9 and theta = -(3pi)/4

hence x = 9cos(-(3pi)/4) " and " y = 9sin(-(3pi)/4)
"----------------------------------------------------------------------"

now cos(-(3pi)/4) = -cos(pi/4)

and sin(-(3pi)/4) = -sin(pi/4)

The 'exact' value of sin(pi/4) = cos(pi/4) = 1/sqrt2
"-------------------------------------------------------------------------"

thus x = -9cos(pi/4) = -9xx1/sqrt2 = -9/2 sqrt2

and y -9sin(pi/4) = -9xx1/sqrt2 = -9/2 sqrt2

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