What are the components of the vector between the origin and the polar coordinate #(12, (-3pi)/4)#?
1 Answer
Mar 4, 2016
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 #