Time and Date Stamps (logged): 17:12:20 06-10-2020 °¶Ÿ°±Ÿ±¯¯µŸ°¯Ÿ±¯±¯ 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:

Directions for Student:

Test Problems:

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Problem Number 1

Calculate the exact value of  cos(tan^-1 ( 2.58 )) and include a diagram showing your reasoning.

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Problem Number 2

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

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Problem Number 3

The signal from a ship comes to you from a direction 22 degrees North of East.   Your buddy 390 km north of you receives the signal from a direction 86 degrees South of East.  How far is the ship from you, and how far from your buddy?  How far is the ship from a straight line connecting your position and your buddy's?

 

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Problem Number 4

If the time between sunrise and sunset on day t of the year is given by    12 + 1.7 sin( 2 `pi / 365 * (t - 80) ) then on what days of the year is the length of the day 12.04 hours?

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Problem Number 5

A person on the other side of a deep gorge stands still while you point laser pointer at the individual's nose.  The person then walks 204 meters perpendicular to your original line of sight and you aim another pointer at the same nose.  The second pointer makes an angle of 10 degrees with the first.  What is the distance across the gorge?

 

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Problem Number 6

If the y coordinate of an object is given by y = 9 sin( 1.611 t ) + -.901, then

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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: Make a table of r = 2 cos(theta) using exact values of 3 theta. Using this table sketch the graph of the function.

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Problem B: Find and graph the 6th roots of -64.

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Problem C: Suppose we both start at the origin, and you move 110 feet at an angle of 135 degrees as measured counterclockwise from the x axis while I move 90 feet at an angle of 55 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?

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Problem D: Express the equation x^2 - y^2 = 4 in polar coordinates.