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r times Secant theta equals -5

put into polar form

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Shawn D. | Mathtastic TutorMathtastic Tutor
5.0 5.0 (9 lesson ratings) (9)

If you want it in polar than George and Bill are both right. But just incase you need it in RECTANGULAR then:


Given: rSec(θ)=-5

we know that Cos(θ)=x/r since Sec(θ) =1/Cos(θ) then Sec(θ)=r/x 

so plug rSec(θ)= r(r/x)

that means that r2/x=-5 

we know by Pythagorean theorem that r2=x2+y2

so we really have (x2+y2)/x=-5

Which is sufficient as for rectangular form. If you wanted the so solve the problem as a function of x only then it would be:


That is if you wanted it in RECTANGULAR FORM... but as for polar form it is already in polar form. 

Bill F. | Experienced Teacher & Tutor in Round Rock, TXExperienced Teacher & Tutor in Round Roc...
5.0 5.0 (1 lesson ratings) (1)

Hi Jen... looks to be like this already is in polar (nor rectangular coordinate) form; just need to rearrange to solve for r:  

r * Sec(θ) = -5;  r = -5/Sec(θ) = -5 / (1/Cos(θ)) = -5Cos(θ)

George C. | Humboldt State and Georgetown graduateHumboldt State and Georgetown graduate
5.0 5.0 (2 lesson ratings) (2)

r sec Θ = -5

-(r/5) = cos Θ

arccos (-r/5) = Θ, Θ lies in the 2nd quadrant and depends upon the value of r.