Review for Test #5

TOPIC #1:Analytic Trigonometry

  1. Evaluate without using a calculator
  1. Find and if and
  2. Find and if and
  1. Find all solutions to the equation in the interval
  1. Prove the Identity

Topic #2:Vectors

  1. Prove and are equivalent by showing they represent the same vector.
  1. R = (-4, 7), S = (-1, 5), P = (0,0) and Q = (3, -2)
  2. R = (-2, -1), S = (2, 4), P = (-3, -1) and Q = (1, 4)
  1. Let u. Find the indicated expressions.
  1. u – v b. 2u – 3w c. d.
  1. Let A = (2, -1), B = (3, 1), C = (-4, 2) and D = (1, -5). Find the component form and magnitude of the vector.
  1. b. c. d.
  1. Find
  1. u = , v =
  2. u = , v =
  3. u = , v =
  4. u = , v =
  5. u =-4i – 9j, v = -3i – 2j
  6. u =7i , v = -2i + 5j
  7. u = 2i – 4j, v = 6j
  1. Find (a) a unit vector in the direction of and (b) a vector of magnitude 3 in the opposite direction.
  1. A = (4, 0), B = (2, 1)
  2. A = (-1, -4), B = (5, 2)
  3. A = (3, 1), B = (-2, 3)
  1. Find (a) the direction angles of u and v and (b) the angle between u and v.
  1. u = , v =
  2. u = , v =
  3. u = , v =

Topic #3:Parametric Equations

  1. Use an algebraic method to eliminate the parameter and identify the graph of the parametric curve.

Topic #4:Polar Equations

  1. Use an algebraic method to find the rectangular coordinates of the point with given polar coordinates.
  1. b. c. d. e.
  1. Rectangular coordinates of point P are given. Find 3 polar points that represent the same point.
  1. (1, 1) b. (3, 5) c. (-2, 3) d. (-1, -3) e. (4, -1)
  1. Convert the polar equation to rectangular form.
  1. r = -2 b. r = c. d.
  1. Convert the rectangular equation to polar form.
  1. b. c. d.
  1. Write the equation of each polar graph. Window is [-5, 5] by [-5, 5]

a. b. c.

  1. e. f.

Topic #5:Complex Numbers

  1. Write the complex number in standard form
  1. b.
  1. d.

Topic #6:Applications

  1. An airplane is flying on a bearing of at 540 mph. A wind is blowing with a bearing of at 55 mph.
  1. Find the component form of the velocity of the airplane.
  2. Find the actual speed and direction of the airplane.
  1. An airplane is flying on a bearing of at 480 mph. A wind is blowing with a bearing of at 30 mph.
  1. Find the component form of the velocity of the airplane.
  2. Find the actual speed and direction of the airplane.
  1. A force of 120 lb acts on an object at an angle of . A second force of 300 lb acts on the object at an angle of . Find the direction and magnitude of the resultant force.
  1. Stewart shoots an arrow straight up from the top of a building with an initial velocity of 245 ft/sec. The arrow leaves from a point 200 ft above level ground.
  1. Write an equation that models the height of the arrow as a function of time t.
  2. How high is the arrow after 4 sec?
  3. What is the maximum height of the arrow? When does it reach its maximum height.
  4. How long will it be before the arrow hits the ground?
  1. Lucinda is on a Ferris wheel of radius 35 ft that turns at the rate of one revolution every 20 sec. The lowest point of the Ferris wheel (6 o’clock) is 15 ft above ground level at the point (0, 15) of a rectangular coordinate system. Find parametric equations for the position of Lucinda as a function of time t in seconds if Lucinda starts (t = 0) at the point (35, 50)
  1. The lowest point of a Ferris wheel (6 o’clock) of radius 40 ft is 10 ft above the ground and the center is on the y – axis. Find parametric equations for Henry’s position as a function of time t in seconds if his starting position (t = 0) is the point (0, 10) and the wheel turns at the rate of one revolution every 15 sec.
  1. Sharon releases a baseball 4 ft above the ground with an initial velocity of 66 ft/sec at an angle of with the horizontal. How many seconds after the ball is thrown will it hit the ground? How far from Sharon will the ball be when it hits the ground?
  1. Brian hits a baseball straight toward a 15 ft-high fence that is 400 ft from home plate. The ball is hit when it is 2.5 ft above the ground and leaves the bat at an angle of with the horizontal. Find the initial velocity needed for the ball to clear the fence.
  1. Spencer practices kicking field goals 40 yd from a goal post with a crossbar 10 ft high. If he kicks the ball with an initial velocity of 70 ft/sec at a angle with the horizontal, will Spencer make the field goal if the kick sails “true”?
  1. An NFL place-kicker kicks a football downfield with an initial velocity of 85 ft/sec. The ball leaves his foot at the 15 yd line at an angle of with the horizontal. What is the maximum height the football gets above the field? What is the total time the ball is in the air?