Find the equation of the tangent line for the following curv

Find the equation of the tangent line for the following curve at?=?/4

r=sin(2?) Must show all steps

Solution

dy/dx=[r\'()sin()+r()cos()]/[r\'()cos()-r()sin()]

=> dy/dx= [2cos(2)sin()+sin(2)cos()]/[2cos(2)cos()-sin(2)sin()] =-1 (at =/4)

at =/4 slope of tangent is -1

x=rsin()=1/2

y=rcos()=1/2

(y-1/2)/(x-1/2) =-1

=>y-1/2=1/2-x

=>x+y=2 is the equation of tangent