



 
Hi Kumi, To sketch the graph I would choose values of θ where I know sinθ. For example θ = 0, ±π/4, ±π/2, π, ±3π/4, ±3π/2. For each find the value of r and then plot the values. For part b. use the facts that r^{2} = x^{2} + y^{2}, x = r cosθ and y = r sinθ. Thus
becomes
Take the denominator on the right side, write it to a common denominator and get
which becomes
Move the y term to the right side, square both sides and simplify. For part d. I would write the centre of the circle in Cartesian form, write the equation of the circle in Cartesian form and then convert it to polar form. Penny  


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