What are the components of the vector between the origin and the polar coordinate (12, (-3pi)/4)?

1 Answer
Jim G.
Mar 4, 2016

((-6sqrt2),(-6sqrt2))

Explanation:

Using the formulae that links Polar to Cartesian coordinates,

• x = rcostheta

• y = rsintheta

Measured clock-wise from the x-axis the angle (-(3pi)/4)
places the point in the 3rd quadrant , where both the sine and cosine ratios are negative.
The related acute angle to (3pi)/4 " is " pi/4

and so cos(-(3pi)/4) = -cos(pi/4)
This is also the case for the sine ratio.

Using 'exact values' for these angles gives.

x = -12cos(pi/4) = -12xx1/sqrt2
and'rationalising' the denominator

x= -12xx sqrt2/2 = -6sqrt2

y = -12sin(pi/4) = -6sqrt2

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