Pre-Calculus Assignment 4

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MATH 115 Quiz4_Fall2018

NAME: ______________________________

By signing my name above, I certify that I have completed this assignment individually,

working independently and not consulting anyone except the instructor.

Instructions for QUIZ 4:

The quiz is worth 100 points. There are 12 problems, some with several parts; point totals are

indicated by each part. It is based on Chapter 10 (Section 10.7) and Chapter 11 (Sections 11.1, 11.2, 11.3, 11.8 and 11.9) of the “College Trigonometry, Stitz and Zeager” text. It is open book and open

notes. This means that you may refer to your textbook, notes, and online classroom materials, but you

must work independently and may not consult anyone (and confirm this with your submission). YOU

MAY USE YOUR GRAPHING CALCULATOR (TI-83/84 or EQUIVALENT, nothing more

sophisticated) TO ASSIST IN GRAPHING OR ANY NUMERICAL CALCULATIONS).

You must show your work. Answers without any work may earn little, if any, credit. You

may type or write your work in your copy of the quiz, or if you prefer, create a document

containing your work. Scanned work is acceptable also.

When you have completed the quiz, upload your solutions file to the Quiz 3 assignment in the

Assignment folder. DUE DATE is NLT 11:59pm EDT, Sunday, September 30.

If you have any questions, please contact me by e-mail.

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1. (8 points). Use the Law of Sines to solve the triangle below by finding the missing parts. Round your

answers to 2 decimal places.

Answer:

Angle "C" = ___ degrees

Side "a" = _ _______

Side "c" = ________

b =10

Angle “B” = 25 o ; Angle “A” = 105

o ; Side b = 10

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2. (8 points). A surveyor standing 63 meters from the base of a building measures the angle to the top of

the building and finds it to be 38°. The surveyor then measures the angle to the top of the radio tower

which is on top of the building and finds that it is 48°. How tall is the radio tower? Round your answer to

2 decimal places.

Answer: Height of Radio Tower = _________ meters

3. (10 points). Use the Law of Cosines to solve the triangle below by finding the missing parts. Round

your answers to 2 decimal places. (HINT: You may also want to use the Law of Sines for the latter part

of the problem).

Answer: Angle "A" = degrees Angle "B" = _degrees Angle "C" = _degrees

6 5

7

63

Building

38o

48 o

Radio Tower

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4. (8 points). Use the Law of Cosines to solve the following problem: Two points A and B are on

opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 50 feet from

point A and 61 feet from point B. The angle ACB is 45°. How far apart are points A and

B? Round your answer to 2 decimal points.

Answer: Distance between A and B = _____ _ feet

5. (6 points). Solve the problem below by referring to Theorem 10.23 (page 795). (HINT: When t = 0,

the position of the weight is -4. Based on this fact, choose the appropriate model, either S(x) or C(x).

“A weight attached to a spring is pulled down 4 inches below the equilibrium position.

Assuming that the frequency of the system is 8/π cycles per second, determine a trigonometric model that

gives the position of the weight at time t seconds.”

Answer: _____________________________________________

A B

C

50 61 45 o

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6. (8 points). Solve the equation below for "x" on the interval [0, 2π). Leave your answers in terms of π.

sin2 x - cos2 x = 0. (HINT: Use a Pythagorean Identity).

Answer: x = ______________________________

7. (8 points). Solve the equation below for "x" on the interval [0, 2π). (HINT: Factor the left hand side).

Leave your answers in terms of π.

cos x + 2 cos x sin x = 0

Answer: x = ______________________________

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8. (12 points). For the given vectors u = < -7, 1 > and w = < 8, 1 > find the indicated expressions.

(a) Find || u + w ||

Answer: || u + w || = _________________________________

(b) Find || u + w|| + || u – w||

Answer: || u + w|| + || u – w|| = ________________________________

9. (6 points). Find the unit vector that has the same direction as the vector v given below.

v = < -12, 5 >

Answer: Unit Vector: < , >

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10. (12 points). Solve the problem below. (HINT: REFERENCE the WEEK 6 SAMPLE PROBLEMS,

Section 11.8, #54).

An aircraft going from Atlanta to Savannah on a heading of 125° from North (N 125°E) is travelling at a speed of 590 miles per hour. The wind is out of the north (that is, it is heading due South) at a speed

of 20 miles per hour.

Find the actual speed and direction (in bearing format) of the aircraft. Express actual speed to the

NEAREST INTEGER MPH, and express the degrees in the BEARING TO THE NEAREST

INTEGER DEGREE.

Answer:

Actual Speed (Nearest integer): ____ mph

Actual Heading (in bearing format, with degrees to the nearest integer): ___ degrees

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11. (8 points). For the given vectors v = < 1, -3 > and w = < 5, 12 > find the PROJwv. That is, find the vector which is the projection of vector v onto the vector w.

Answer: PROJwv = <_______ , _______>

12. (6 points). Write a vector v in the form < , > whose magnitude ||v|| and direction angle θ are given

below. (HINT: Let P(x,y) be the coordinates of the point at the tip of the vector. Form a right triangle

and use trigonometry).

||v|| = 8; θ = 30 o

Answer: Vector v = < _______ , ________ >