MATH 126 Calculus II Learning Goal Activity 11 4 12 1 Name Due Date November 17 2023 11 59pm On Canvas LEARNING GOAL values and or rst sketching the graph in the r plane to sketch the graph of a polar equation r f in the xy plane by making a table of 1 a Use the graph of the equation r f in the r plane on the left to sketch the graph of the same equation in the xy plane on the right 6 3 2 2 3 5 6 7 6 4 3 3 2 5 3 11 2 6 2 1 x 2 1 b Sketch the graph of r 2 cos 3 in the xy plane by rst sketching its graph in the r plane 6 3 2 2 3 5 6 7 6 4 3 3 2 5 3 11 2 6 2 1 x 2 1 c Sketch the graph of r 1 2 sin in the xy plane by rst sketching its graph in the r plane y 2 1 1 2 1 2 y 2 1 y 3 2 1 6 3 2 2 3 5 6 7 6 4 3 3 2 5 3 11 2 6 2 1 1 x 2 1 r r r 2 1 6 1 2 2 1 6 1 2 3 2 1 6 1 1 LEARNING GOAL to nd the area bounded by polar curves by rst nding the rays and bounding the area and then using the formula r2 d cid 90 1 2 2 Find the areas of the following regions a the area enclosed by the polar curve r 2 for 0 2 b the area of one petal of the graph of r 2 cos 3 c the area of the inner loop of the graph of r 1 2 sin 2 LEARNING GOAL to nd the area bounded by two polar curves by rst nding the rays and bounding the area and then using the formula f 2 g2 d 3 Find the areas of the following regions a the region inside the graph of r 1 sin but outside the graph of r 1 cid 90 1 2 b the region inside the graph of r 2 sin but outside the graph of r 1 3 LEARNING GOAL to recognize and use the Triangle law uently and exibly in a variety of tasks 4 The vectors u and v are depicted below Use the Triangle Law to depict and label each vector in the depiction for the following vectors a 2u b v u c u v d 2u 1 2 v u v 4 LEARNING GOALS to know to scale and or sum vectors by scaling and or summing appropriate compo nents standard basis vectors to nd the magnitude of a vector as the square root of the sum of the squares of its components to understand the de nitions of and how to produce use special vectors such as position vectors and unit vectors 5 For each pair of vectors given do the following Calculate 3a 2b Find a unit vector eb sharing its direction with b a a and b are position vectors for the points A 1 2 3 and B 2 1 respectively b a has representation AB where A 1 3 and B 2 1 are points in R2 and b 3i 2j c a is a unit vector parallel to the line y 4x and b cid 104 4 16 cid 105 6 Let A 2 4 and B 4 0 be points in R2 y a Plot points A and B b Sketch the position vector ponent form OA and write it in com c Sketch the position vector ponent form OB and write it in com x d Sketch the vector form AB and write it in component 5