Pre-Calculus



Pre-Calculus

Web Chapter 6 Test

1). Let [pic], [pic]. Find the vector [pic]. Then find its magnitude and direction.

2). An airplane is flying on a bearing of [pic]at 420 mph. A wind is blowing with a bearing of [pic] at 30 mph. Find the actual speed and direction of the plane (in bearings).

3). Find all possible polar coordinates for the rectangular point (-2, 5).

4). Given vertices A(-4, 5), B(1, 10), and C(3, 1) find the interior angles of the triangle ABC using vectors.

5). Evaluate [pic]. Express your answer in trigonometric form.

6). Three forces with magnitudes of 120, 75, and 60 lbs., act on an object at angles of 70˚, 150˚, and -10˚ respectively. Find the direction and magnitude of the resultant force.

7). Analyze the graph of the polar curve [pic].

8). Convert the equation [pic] to rectangular coordinates and describe the graph.

9). Find all of the petal lengths and the angles associated with them for the polar equation [pic]. Answers should be written as ordered pairs.

10). The locations, given in polar coordinates of two planes approaching the Toronto airport are [pic] and [pic]. Find the distance between the planes.

11). Eliminate the parameter, find the endpoints, and describe the graph for the parametric equations.

[pic]

12). Find the work done on an object if a force of 25 lbs is applied in the direction [pic] in moving the object 4 feet along the positive x-axis.

13). Find the unit vector in the direction of [pic] and find a vector u in the same direction as vector v, where [pic] = 3.

14). Find the 4th roots of the complex number 3 + 3i. Answer should be left in trig form.

15). Cory is sitting on a sled on the side of a hill inclined at [pic]. The combined weight of Cory and the sled is 175 lbs. What is the magnitude of force required to keep Cory from sliding down the hill?

16). Convert the equations [pic] and [pic]to rectangular coordinates and describe the graph.

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