**Find the slope of the tangent line to the given polar curve at the point specified by the value of Ɵ using the exact answer: r = 2 - sinƟ, Ɵ = π/3 ?**

**Answer:**

In polar coordinates, we know that

x=rcost

y=rsint

Then dx/dt=-rsint and dy/dt=rcost,

(dy/dt)/(dx/dt)=dy/dx=(-rsint)/(rcost)=-cott

since we want to find y’ at the pint t=pi/3 then our answer is

-cot(pi/3)=-1/(sqrt(3))