Trigonometry homework help. PURPOSE of the Final Assignment
The purpose of this assignment is for you to identify and reflect on your areas of strength and areas of
weakness in some of the core topics of Trigonometry. Because of the remote learning situation, we were
not able to have a traditional Exam 3 or a traditional Final Exam. Since moving to remote learning,
you have always had full access to a list of identities, perhaps a unit circle diagram, as well as other
resources and notes for use while doing your work for this course. In your future coursework- Calculus,
Physics, and perhaps other courses, you will be expected to know Trigonometry during exams and in
class, without the use of a calculator, without the use of a unit circle diagram, and without the use
other resources.
I hope that this assignment will help you to honestly assess what you know and what you don’t
know so you can do the work to prepare for success in future courses.
Steps to Complete for the Final Assignment
Step 1: Print the Self-Test. Take this Self-Test as though you are in an exam setting.
• No notes, no unit circle, no resources whatsoever. Calculator only for the
calculator-ready question (#13). This is really important! If you have those resources
during your Self-Test, you will not know what you really know!
• If you prefer, you may complete the exam in digital format (using a tablet or similar). Or
if you do not have a printer, you can write your solutions, in order, on regular paper.
Step 2: Once you’ve completed the Self-Test, use your resources- notes, textbook, class website, external
websites, to check your work and correct any errors in your original work.
Step 3: Write a reflection paper discussing your assessment of your knowledge, what topics you feel you
have mastered, and what topics you feel you’ll need to work on more before using the ideas in
future classes. Be sure to mention any courses you’ll be taking that require Trigonometry as a
prerequisite. Your paper should be 1.5 − 3 pages in length, typed, with correct grammar and
spelling. Be honest with your assessment.
Submit as a pdf:
1. Your Self-Test after you’ve corrected any errors you might have made. I do not need to see your
original Self-Test, only the corrected version.
2. Your reflection paper.
Submit both the Self-Test and Reflection Paper to Dr. Davis via email by
6:00pm on Thursday, May 14.
If you are having technical difficulties, contact Dr. Davis via email as soon as possible. The earlier
the better. Do not wait until the last minute to submit your Final Assignment.
Grading for the Final Assignment:
Your grade on the final assignment will be out of 200 points. The first 120 will come from your correct
solutions to the Self-Test. The remaining 80 points are for the reflection paper.
To earn full points on the reflection paper, ask yourself:
• Is my name on the reflection paper?
• Is my reflection paper the correct length?
• Is it typed? (if you do not have a computer and need to hand write your paper, please contact
me before submitting your assignment)
• Have I used correct spelling and grammar?
• Have I addressed the questions being asked at a reasonable depth?
2
Name: Section:
Please write your name on every page.
Self-Test – Trigonometry Spring 2020
• Do not use your calculator on any problem except problem #13.
• For the first try at this Self-Test, do not use notes, textbook, reference sheets, or any resources.
• Show all of your organized thought processes. If you used extra scratch paper to do your work,
include it with your exam and label each problem’s work with the correct problem number.
Final answers with no support on how you arrived at the answer will not receive full credit.
• Give final answers as exact values. Any decimal approximations on any problem except #13 will
receive zero credit.
Number Points Points Scored
1 12
2 12
3 9
4 6
5 6
6 8
7 8
8 16
9 12
10 6
11 9
12 8
13 8
Total 120
Name: Section:
No Calculator allowed on Part I. A complete solution includes your work and/or reasoning.
1. Trig function definitions. Write the definitions of all six trig functions. State both the
“opp, adj, hyp,” definition and the ‘x, y, r” definition.
2. Trig values for the most common angles. For the given values of θ, determine exact values
for sin θ and cos θ and fill in the table.
θ → π
π
2
π
3
π
4
π
6
sin θ
cos θ
4
3. Graphs of Trig and Inverse Trig Functions. Below are graphs of the six trig functions and
three inverse trig functions. Match each function with its graph from choices A – I.
-2 p – 3 p
2 -p – p
2
p
2 p 3 p
2 2 p
-1.0
-0.5
0.5
1.0
-2 p – 3 p
2 -p – p
2
p
2 p 3 p
2 2 p
-6
-4
-2
2
4
6
-2 p – 3 p
2 -p – p
2
p
2 p 3 p
2 2 p
-5
5
-2 p – 3 p
2 -p – p
2
p
2 p 3 p
2 2 p
-6
-4
-2
2
4
6
-2 p – 3 p
2 -p – p
2
p
2 p 3 p
2 2 p
-1.0
-0.5
0.5
1.0
-2 p – 3 p
2 -p – p
2
p
2 p 3 p
2 2 p
-6
-4
-2
2
4
6
A
B
C
D
E
F
-1.0 -0.5 0.5 1.0
– p
2
– p
4
p
4
p
2
-10 -5 5 10
– p
2
– p
4
p
4
p
2
-1.0 -0.5 0.5 1.0
p
4
p
2
3 p
4
p
G
H
I
y = sin x y = csc x y = arcsin x
y = cos x y = sec x y = arccos x
y = tan x y = cot x y = arctan x
5
4. Converting degrees to radians. Convert each angle to radians.
(a) 210◦
(b) 240◦
(c) 420◦
5. Trig values for angles whose reference angles are special angles. Find the exact value for
each expression.
(a) sin( 5π
6
)
(b) cos( 5π
4
)
(c) tan( 11π
6
)
6
6. Trig values for quadrantal angles Find the exact value for each expression.
(a) sin( π
2
)
(b) cos(0)
(c) cos(π)
(d) sin( 3π
2
)
7. Solving an equation involving trig functions. Solve the equation for x on the interval
0 ≤ x ≤ 2π.
16 cos x sin x + 8 sin x = 0
7
8. Fundamental Identities. State the following fundamental identities.
(a) Quotient Identities (two of these)
(b) Reciprocal Identities (three of these)
(c) Pythagorean Identities (three of these)
9. Using Trig Identities. Simplify each expression completely. Your final answer will be a
number, a single trig function, or a power of a trig function.
(a) sec2 x − tan2 x
csc x
(b) (sin x + cos x)
2 − 2 sin x cos x
8
10. Inverse Trig functions. State the domain and range for y = sin−1
(x), y = cos−1
(x), and
y = tan−1
(x).
11. Inverse trig expressions. Find the value of each expression.
(a) arcsin(sin( 3π
4
))
(b) cos(arctan(−
√
3))
(c) sin(arccos( −
√
3
2
))
9
12. Modified Sine and Cosine Graphs. Determine a function of the form y = a cos(b(t−d))+c
that yields the graph given below. (see figure)
13. Solving a right triangle. You MAY use your calculator on this problem ONLY.
Solve the right triangle. That is, find values for all the labeled sides and angles. (see
figure)
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Trigonometry homework help