What is the Cartesian form of ( 7 , (-35pi)/12 ) (7,−35π12)?

1 Answer
A. S. Adikesavan
Apr 7, 2016

(x, y) = (-7 cos (pi/12), -7 sin (pi/12)) = ( -6.7615, -1.8117 )(x,y)=(−7cos(π12),−7sin(π12))=(−6.7615,−1.8117) nearly.

Explanation:

x = r cos theta and y = r sin thetax=rcosθandy=rsinθ.
Here, r = 7 and theta=-35pi/12θ=−35π12.

Note that cos (-x) = cos x, sin (-x)=-sinx, cos(3pi-x)=-cos x and sin(3pi-x)=sin xcos(−x)=cosx,sin(−x)=−sinx,cos(3π−x)=−cosxandsin(3π−x)=sinx.
The angle 3pi-x3π−x is in the second quadrant.

cos (-35pi/12)=cos (pi/12-3pi)=cos(3pi-pi/12)=-cos(pi/12)cos(−35π12)=cos(π12−3π)=cos(3π−π12)=−cos(π12).
sin (-35pi/12)=sin (pi/12-3pi)=-sin(3pi-pi/12)=-sin(pi/12)sin(−35π12)=sin(π12−3π)=−sin(3π−π12)=−sin(π12)

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