Question

please help me and show all the steps and make sure it's correct

[10pts.) 5. Find dy and the equation of the tangent line at the point (x,y)=(-2, 0) on the curve r = 21-sin(@)). Include a graph of the polar curve with the orienation indicated. dx [10 pts.) 6. Graph the polar equations r = 5 cos(30) and r = 3cos() for --/2S15 /2. Label any key points needed to find the area that lies in the common interior of the two. Show the setup of any equation needed and you should use technology to solve the equation and find any intersection points. Set up the integral(s) and show all steps to integrate and evaluate manually to find the area.

Answer 1

In polar ar coordinates i 0 X = r coso r sino y Given r-911-sino) 2 11 from r Vae sino ty y Jocery² Jeet y? Ja² ty? 012 x² + y² - a [ Joe'ty? -y] Differentiating both side writ. s 24+ 2 ube?+y? x + ydy De ty z turtya q + Oy dy - gat qu dy dae dze dy dre LS du dy de y Johtye dy y ya da

(sto, yo) 1-9,0) Naty? - 1] se lyladyo -y-Jan-ya dua Given point Ne-9) ](-2) (2-1)(-2) (0-0-1-95) dy don (-2) dy dre dy 1 da Tangent is given by : (y-yo) dy dy In-Ho) (1) (2-6-2)] cy- -0) y eta