Sec theta = 2 to rectangular coordinates??

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Answer 1 · 2018-02-26T15:23:06

See below.

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Identity.

#color(red)bb(secx=1/cosx)#

#1/cos(theta)=2#

#cos(theta)=1/2#

#theta=arccos(cos(theta))=arccos(1/2)=>theta=pi/3, (5pi)/3#

For:

#0<=theta<=2pi#

From the above diagram, we can see that:

#x=rcos(theta)#

#y=rsin(theta)#

So coordinates will be:

#(rcos(pi/3),rsin(pi/3))#

#(rcos((5pi)/3),rsin((5pi)/3))#

Without knowing the radius we can't go any further than this.

If this is on a unit circle then the radius is #1# and:

#cos(pi/3)=1/2# , #sin(pi/3)=sqrt(3)/2#

#cos((5pi)/3)=1/2# , #sin((5pi)/3)=-sqrt(3)/2#

Coordinates:

#(1/2,sqrt(3)/2)# , # (1/2 , -sqrt(3)/2)#