How to draw graph of $r= 3sintheta+4costheta$ ?

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Answer 1 · 2018-03-12T08:58:41

Draw a circle with a center at $(2,3/2)$ with a radius of $2.5$ .

Multiply both sides by $r$ to get $r^2=3rsintheta+4rcostheta$

$r^2=x^2+y^2$
$3rsintheta=3y$
$4rcostheta=4x$

$x^2+y^2=3y+4x$

$x^2-4x+y^2-3y=0$

$(x-2)^2-4+(y-3/2)^2-9/4=0$

$(x-2)^2+(y-3/2)^2=4+9/4=25/4$

Draw a circle with a center at $(2,3/2)$ with a radius of $2.5$ .

How to draw graph of r= 3sintheta+4costhetar= 3sintheta+4costheta?