precalculus questions

Ch 6-10 Test ~ Form H Trigsted 1st ed Created Spring 2018 Fast Track page 1

MATH 2412 ~ PreCalculus Instructor: Villarreal Chapter 6‐10 Test Form H Answer each question carefully and completely showing as much work as possible. For multi-stepped problems you must show your work in order to receive full credit. Using only a calculator to find the answer is not sufficient. In this case, you must use algebra to prove your answer is correct. Unless stated otherwise, the calculator should only be used to check your answer. Make sure that all answers are in simplest form and that you use the correct symbols. If indicated, you must use the requested method in order to receive full credit.

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1. Determine the specific solutions (if any) on the interval [0, 2π).

2cos 1 sin 2. Find the exact value of the expression or state that it does not exist.

sin 6 11

Ch 6-10 Test ~ Form H Trigsted 1st ed Created Spring 2018 Fast Track page 2

3. A ship set sail from port at a bearing of N 24° W and sailed 35 miles to point B. The ship then turned (counterclockwise) and sailed an additional 42 miles to point C. Determine the distance from port to the ship (point C) if the bearing from the port to point C is N 49° W.

4. Consider the point (-2, ) in the polar plane.

a. Plot the point in the polar plane. Be sure to clearly mark the polar axis and the pole.

b. Convert the polar coordinates to rectangular coordinates.

c. Find two different representations of the point P that have the specified conditions:

 r > 0, 2 0  r < 0, 2 4

Ch 6-10 Test ~ Form H Trigsted 1st ed Created Spring 2018 Fast Track page 3

5. Convert the rectangular equation 6 8 to a polar equation. Express r in terms of .

6. Determine the standard polar form of the complex number 4 4 . Write the argument in terms of radians using exact values.

7. Find and if 6 and 7 Write your answers in standard polar form with the argument in radians.

Ch 6-10 Test ~ Form H Trigsted 1st ed Created Spring 2018 Fast Track page 4

8. Find 3 cos sin and write the answer in rectangular form.

9. Determine the component representation and magnitude of the vector having the initial point P(-2, 3) and the terminal point Q(4, 11).

10. An airplane was heading due east at 340 mph in still air and encountered a 46 mph headwind blowing in the direction S 38° W. Determine the resulting ground speed of the plane and its new bearing.

Ch 6-10 Test ~ Form H Trigsted 1st ed Created Spring 2018 Fast Track page 5

11. A mover in a moving truck is using a rope to pull a 397 lb box up a ramp that has an incline of 30°. What is the force needed to hold the box in a stationary position to prevent the box from sliding down the ramp? What is the magnitude of the force pushing against the ramp?

12. Represent the vector v in the form ai + bj whose magnitude and direction angle are given

‖ ‖ 7; 240° 13. Determine if the given vectors are orthogonal, parallel, or neither. Give a mathematical reason

for your answer.

u = 4i – 5j, v = 10i + 8j