Find the center of the circle `x=-1+2costheta,y=3+2sintheta`

Find the equations of the tangent and the normal to the curve 4x^2+9y^2=36 at (3costheta,\ 2sintheta) at indicated points.

Evaluate (1-costheta)^2+(sintheta)^2

Evaluate (1-costheta)^2+(sintheta)^2

Find the slopes of the tangent and the normal to the curve x=a(theta-sintheta) , y=a(1+costheta) at theta=-pi//2

Find the slopes of the tangent and the normal to the curve x=a(theta-sintheta),\ \ y=a(1-costheta) at theta=pi//2

Find the equations of the tangent and the normal to the curve x=theta+sintheta , y=1+costheta at theta=pi//2 at indicated points.

Evaluate [(1+costheta)/sintheta]^2

If tantheta=(4)/(3) , then find the value of (3sintheta-2costheta)/(3sintheta+5costheta)

If the angle theta is acute, then the angle between the pair of lines given by (costheta-sintheta)x^(2)+2(costheta)xy+(costheta+sintheta)y^(2)=0 is