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:

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