Pre-Calculus Homework
1
MATH 115 Quiz3_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 3:
The quiz is worth 100 points. There are 12 problems, some with several parts; point totals are
indicated by each part. It is is based on Chapter 10 (Sections 10.2 through 10.7) 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 23.
If you have any questions, please contact me by e-mail.
-------------------------------------------------------------------
1. (6 points). Use the Pythagorean Theorem to find the length of the missing side of the right triangle
shown below. Then find the sine of the indicated angle. Give an exact answer by simplifying and
leaving your answer in radical form, rationalizing the denominator if necessary.
Answer: sin θ = ____________
4
5 C
B
A θ
2
2. (8 points).
(a). θ is an acute angle and the sin θ and cos θ are as indicated below. Using this
information, find the tan θ.
𝒔𝒊𝒏 𝜽 = 𝟓
𝟕 ; 𝒄𝒐𝒔 𝜽 =
𝟐√𝟔
𝟕
Answer: tan θ = ____________________________________
(b). θ is an acute angle. Using the given information, find the exact value of sin θ.
𝒄𝒐𝒔 𝜽 = 𝟒
𝟕 ; 𝒕𝒂𝒏 𝜽 < 𝟎
Answer: sin θ = ____________________________________
3. (10 points). A building 230 feet tall casts a 70 foot long shadow. If a person stands at the end of the
shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the
building? Assume the person's eyes are 5 feet above ground level. Give your answer to two (2) decimal
places.
Answer: Angle of elevation (in degrees) to top of building = __________ degrees
3
4. (10 points). A point on the terminal side of angle θ is given below. Find the exact value (i.e., leave
your answers in either fractional form or with a simplified radical) of each of the trigonometric
functions of θ.
(-15, 36)
(a) sin θ = ________________; (b) cos θ = _____________________
(c) tan θ = ________________; (d) cot θ = _____________________
(e) csc θ = ________________; (f) sec θ = _____________________
5. (8 points). Verify the identity shown below by starting with one side and by using appropriate
identities, arrive at the expression on the other side.
csc u - sin u = (cos u) ∙ (cot u)
4
6. (8 points). Find all solutions of the equation shown below. (Note: By “all” solutions we mean not
just restricted to [0, 2π)).
2 cos θ - √𝟑 = 0
Answer: θ = _____________________________________________
7. (10 points). For the function below, determine the (a) amplitude; (b) period; (c) phase shift (and
indicate shift left or shift right); and (d) vertical shift. SKETCH AT LEAST ONE CYCLE OF THE
GRAPH ON THE AXES BELOW.
𝒚 = 𝟏
𝟒 𝐬𝐢𝐧(𝟑𝒙 + 𝝅) − 𝟐
Answer:
(a) Amplitude: ______________
(b) Period: _______________
(c) Phase Shift: _______________ Shift is LEFT / RIGHT (CIRCLE ONE)
(d) Vertical Shift: _______________
5
8. (8 points). Find all values of "x" on the interval [0, 2π) which solves the given equation. (HINT:
Move all terms to the left side, with a"0" on the right. Factor the left hand side and use the Zero
Product Principle!!)
2 sin 2 x = sin x
Answer: x = _________________________________
6
9. (8 points). Find the exact value of the expressions below:
(a). 𝒂𝒓𝒄 𝒔𝒊𝒏 √𝟑
𝟐
Answer: ___________________________
(b). 𝒂𝒓𝒄 𝒄𝒐𝒔 (− √𝟐
𝟐 )
Answer: ___________________________
10. (6 points). Find the exact value of the expression below. (HINT: It might help to draw a right
triangle and determine the lengths of the sides).
𝒄𝒐𝒔(𝒂𝒓𝒄 𝒔𝒊𝒏 𝟑
𝟓 )
Answer: ___________________________
7
11. (10 points). A radio transmission tower is 220 feet tall. How long should a guy wire be if it is to be
attached 5 feet from the top and is to make an angle of 26° with the ground? Give your answer to the
nearest tenth of a foot.
Answer: Length of guy wire = ___________________________feet
12. (8 points). Use reference angles to find the exact value of the expression below. Give an exact
answer (i.e., leave in radical).
𝒔𝒊𝒏 𝟓𝝅
𝟑
Answer: ___________________________