Time and Date Stamps (logged): 05:32:07 12-05-2008
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Precalculus II
Precalculus II Test 2
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
Find all the solutions where 0 < `theta < 2 `pi of the equation 3
tan( 7 `theta - 3 `pi/4) = -.7008.
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Problem Number 2
If you drive for 3600 meters along a hill and travel 931.7 meters in the vertical
direction and 3477 meters in the horizontal, then what is the angle of elevation of the
hill?
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Problem Number 3
If a, b and c designate the lengths of the sides of a triangle and `alpha, `beta
and `gamma the angles opposite these respective sides, then find the area of any possible
triangle(s) defined by
- a = 5.3, b = 4.8, `gamma = 15 degrees
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Problem Number 4
Graph the damped vibration given by y = e^(- 1 x / `pi) sin( 2 x ).
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Problem Number 5
Show that cos(sin^-1(u)) = `sqrt(1-u^2).
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Problem Number 6
Standing at the shore of a river beneath a bridge of known length 480 feet, you
determine that the angle of elevation of a line of sight to one end of the bridge is 80
degrees, while the angle of elevation of your line of sight to the other end is 83
degrees. How high is the bridge?
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The remaining problems, Problems A - D, are optional for distance students. Not all these topics have been covered by the distance class.
Problem A: Express the equation r = 2 sin(theta) - 3 tan(theta) in rectangular coordinates.
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Problem B: Find all sides and angles of a triangle with sides of lengths 5 and 7, and angle 53 degrees between these sides.
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Problem C: Vector u runs from the initial point (3, 5) to the terminal point (-4, 2).
What is the magnitude of this vector, and what angle does it make with the positive x direction? Vector v runs from the same initial point to terminal point (7, 4). What is the angle between u and v? What is the angle and magnitude of the vector u + v?
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Problem D: Suppose we both start at the origin, and you move 110 feet at an angle of 235 degrees as measured counterclockwise from the x axis while I move 190 feet at an angle of 155 degrees as measured counterclockwise from the x axis. Sketch a set of x-y coordinate axes. Show your path from the origin to your final point, and my path from the origin to my final point.
Complete a triangle by sketching a line segment from your final point to mine.
Label the known sides and angles of that triangle.
Do you have enough information to find the distance from your final position to mine? If so, how would you go about this?