Precalculus II

Time and Date Stamps (logged): 17:12:20 06-10-2020 ｰｶ涓ｱ浤ｯｯｵ涓ｯ浤ｯｱｯ Precalculus II

Precalculus II Test 1

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

Using transformations sketch the graph of y = -1.7 cos(-5 `pi t + `pi / 4 ).

Problem Number 2

Establish or refute the proposed identity (sec(a) – 1)(sec(a) + 1) = tan^2(a).

Problem Number 3

If an arc of a circle of radius 9.75 is subtended by a central angle of 12 radians, then what is the length of the arc?

Problem Number 4

Without using a calculator find the exact sine and cosine of each of the following angles: Accompany your work with a sketch and an explanation.

210 deg
30 deg
135 deg
13 `pi / 6
7 `pi / 3
9 `pi / 4

Problem Number 5

A Ferris wheel has diameter 44 feet. It takes 33 seconds for the wheel to complete a revolution. How fast is the rim of the wheel moving?

Problem Number 6

Each of the functions y = sin(x), y = cos(x), y = sin(x + `pi/2), y = cos(x + `pi/2), y = -sin(x+`pi) and y = -cos(x + `pi) can be represented by one of two graphs. Sketch these two graphs and tell which functions go with each. Explain in terms of the circular definitions of the trigonometric functions why the functions that go with y = sin(x) do so, and why those that go with y = cos(x) do so.

Problem Number 7

List the formulas for sin(a/2), cos(a/2) and tan(a/2).

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Problem A: Explain in detail how we derive the values of the sine and cosine functions of 30 and 60 degrees using a 30-60 right triangle with hypotenuse 1. Explain how we know the lengths of two the sides from basic geometry, and how we then use the Pythagorean Theorem to find the length of the third side. Then explain in terms of the definition of the sine function how we use this triangle to find the exact value of the sine of 60 degrees.
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Problem B: Sketch the unit circle, indicate all angles which are multiples of pi/4 and indicate the x and y coordinates of the unit-circle point corresponding to each multiple. Use these values to make a table of sin(theta) vs. theta, and a table of cos(theta) vs. theta. Sketch on a single set of clearly labeled coordinate axes the graph of each function. Be sure the horizontal-axis intercepts of the graph are labeled.
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Problem C: A certain town is 622 miles north and 407 miles east of an airport. How far and in what direction, as measured counterclockwise from the easterly direction, would an airplane have to fly to reach that town?
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