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Fall 2016 MATH 108 Quiz 4

Problem 1. 2 pts. Convert the polar point (8, 3π/4) into rectangular coordinates (x,y). Compute the coordinates exactly.

Problem 2. 2 pts. Convert the rectangular point (-6, 0) into polar coordinates in the form

(r, θ). .

Problem 3A. 6 pts. Fill in the blanks in the listed polar points (r, θ) below, to satisfy the polar function r = 2 - 4 cos (θ/2)

Given θ = -π/3, find r: ( ____, -π/3)

Given θ = 0, find r: ( _____, 0)

Given r = 0, find θ: ( 0, ____ ) (Note that there are an infinite number of correct answers for this and you only need to find one.)

4 pts. 3B. Graph the polar function r = 2 - 4 cos (θ/2)

You can plot by hand, with an online grapher, or graphing calculator. Locate and mark the three points you found above on your graph.

Problem 4. 10 pts.

2 pts. A. Vector 𝑣⃗ has a magnitude of 20 and when drawn in standard position, makes an angle of 16° with the positive x axis. Draw vector 𝑣⃗ and resolve it into its component form. Round your answers to the nearest hundredth.

2 pts. B. Vector 𝑤⃗⃗⃗ has a magnitude of 14 and when drawn in standard position, makes an angle of 126° with the positive x axis. Draw vector 𝑤⃗⃗⃗ and resolve it into its component form. Round your answers to the nearest hundredth.

1 pt. C. Draw the vector sum 𝑣⃗ + 𝑤⃗⃗⃗ in standard position.

2 pts. D. Find the component form of 𝑣⃗ + 𝑤⃗⃗⃗.

1 pt. E. Find the magnitude of 𝑣⃗ + 𝑤⃗⃗⃗

2 pts. F. Find the angle the vector sum 𝑣⃗ + 𝑤⃗⃗⃗ makes with the positive x axis.

Problem 5. Vector 𝑢⃗⃗ is < -2, -8>. Vector 𝑣⃗ is < 3, 2 >

2 pts. 5A. Find the dot product 𝑢⃗⃗ ∙ 𝑣⃗

4 pts. 5B. Find the angle θ between 𝑢⃗⃗ and 𝑣⃗. θ should be an angle between 0° and 180°, rounded to the nearest hundredth.