What is the Cartesian form of #( -2, (-7pi)/8 ) #?

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Answer 1 · 2018-07-27T13:58:05

Cartesian coordinates are

#(x, y) \equiv(1.8477, 0.765)#

The cartesian coordinates #(x, y)# of the given point #(r, \theta)\equiv(-2, -{7\pi}/8)# are given as

#x=r\cos\theta#

#=-2\cos({-7pi}/8)#

#=2\cos({pi}/8)#

#=1.8477#

#y=r\sin\theta#

#=-2\sin({-7pi}/8)#

#=2\sin({pi}/8)#

#=0.765#

hence the cartesian coordinates are

#(x, y) \equiv(1.8477, 0.765)#

Answer 2 · 2018-07-27T13:59:44

Cartesian coordinates are #(1.8478,0.7654)#

For a polar form coordinates #(r,theta)#

Cartesian form is #(rcostheta,rsintheta)#

Hence, for #(-2,(-7pi)/8)#

Cartesian form is #(-2cos((-7pi)/8),-2sin((-7pi)/8))#

i.e. #(-2(-cos(pi/8)),-2(-sin(pi/8))#

and as #sin(pi/8)=1/2sqrt(2-sqrt2)=0.3827#

and #cos(pi/8)=1/2sqrt(2+sqrt2)=0.9239#

and Cartesian coordinates are #(1.8478,0.7654)#