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MA003 Final Exam - Precalculus II
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MA003 Final Exam - Precalculus II
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25 Questions

1. A patient's blood pressure is modeled by the function

. Systolic blood pressure is the maximum value of this function and diastolic pressure s the minimum value. If blood pressure is written as systolic/diastolic, what is the blood pressure for the given patient?
2. An airplane heads due north at 300 mph. There is a 40 mph crosswind flowing from the southwest . What are the true speed and direction of the airplane? (Bear in mind that direction is measured from North in the clockwise direction.)
3. If a turntable rotates at 75 revolutions per minute, what is its angular speed (in radians per second)?
4. The phase of the moon can be measured astronomically by the fraction of the lunar disc that is lit. If



represents the angle between the sun, earth, and moon, then the phase of the moon can be represented by the function

. Determine the angle that that corresponds to a crescent moon (P = .25).
5. Find exact values for the (i) sine, (ii) cosine, and (iii) tangent of

.
6. A 3500 ft. mountain is inclined

from the horizontal (i.e. the face of the mountain and the ground form a

angle). A cable car is installed at a point 1000 ft. from the base of the mountain. What is the minimum amount of cable required to reach the top of the mountain, to the nearest foot?
7. Consider this:
is a point given in polar coordinates. Find its rectangular coordinates.
8. A man leaves home, walks 4 miles west and then 2 miles southeast. If he returns directly home (i.e. walking the straight line from his current location to his home) what is his total distance traveled, to the nearest hundredth mile?
9. If the minute hand of a clock is 8 inches long, what distance will its tip move in 12 minutes?
10. Convert

to radian measure, giving the answer in terms of

.
11. Which of the following is equivalent to

?
12. Which of the following is equivalent to

?
13. For

, which of the following is equivalent to

?
14. One leg of a right triangle measures 6 units. The angle adjacent to that leg measures

radians. Find the measure of the hypotenuse of the triangle to the nearest hundredth.
15. Find all solutions of the equation

.
16. A ceiling fan with 16 in blades rotates at 45 rpm. Find the linear speed of the tips of the blades in in/min.
17. Find the exact value of

, if it is defined.
18. Express the complex number

in trigonometric form.
19. How many petals does the rose curve

have?
20. Which algebraic expression is equivalent to

?
21. Which of the following is equal to
?
22. The hypotenuse of a right triangle measures 10 units. One of its non-right angles measures

. Find the measure of the side opposite of that angle. Round your answer to the nearest hundredth.
23. Find the coordinates of a point on a circle with radius 8 corresponding to an angle of

. Leave your answer in terms of sine and cosine, and write the answer as an ordered pair.
24. Solve the triangle for the missing sides, or state that no triangle satisfies the condition. Angle A =

, a = 70 (across from angle A) and b= 122.
25. Find a parametrization of the line segment beginning at the point (3, 2) and ending at the point (-1, 4). Specify the bounds for t.

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