Mathematics

Isaac Obrien

1 March, 07:27

3. (This is Lesson 33 Problem 2 which is due tonight.) For the graph of r = sin 3θ: (a) Draw the part of the graph from θ = 0 to θ = π 6. (Hint: as the angle rotates from 0 to π 6, r increases from 0 to 1.) (b) Draw the part of the graph from θ = π 6 to θ = π 3. (Hint: as the angle rotates from π 6 to π 3, r decreases from 1 to 0.) (c) Draw the part of the graph from θ = π 3 to θ = π 2. (Hint: as the angle rotates from π 3 to π 2, r decreases from 0 to - 1; remember what it means when r is negative.) (d) Now draw the part of the graph from θ = π 2 to θ = π. (e) Finally, draw the part of the graph from θ = π to θ = 7π 6; what do you notice?