Trigonometry

I need this done in no less than an 1hr and 30min

Math 1120 Final Exam

You have 120 minutes to complete this exam and upload a scanned copy of your work into Black-
board.
Put your work and answers on your own paper; you do NOT need to recopy the original problems.
You may use your notes but are not allowed to ask for help from other people or look up any answers
online.
You will be graded mainly on your work so make sure to do the problems as they are stated and
show all of your work!

You must solve these problems as shown in THIS class and show all of your work.

1. (9 points) Carefully graph one period of y = −2 cos(2x− π).
Clearly indicate the maximum and minimum y-values on the y-axis and clearly indicate on
the x-axis the x-values corresponding to the maximum, minimums, and zeroes (x-intercepts)
of the function.
DO NOT USE YOUR GRAPHING CALCULATOR. DO NOT CALCULATE
PERIOD AND PHASE SHIFTS USING SET FORMULAS: SHOW ALL WORK
USING METHODS TAUGHT IN THIS CLASS.

2. (9 points) Carefully graph one period of y = 5 csc(3x+ π).
Clearly indicate the local maximum and minimum y-values on the y-axis, and on the x-axis
the x-values corresponding to the vertical asymptotes and local maximums or minimums of
the function.
DO NOT USE YOUR GRAPHING CALCULATOR. DO NOT CALCULATE
PERIOD AND PHASE SHIFTS USING SET FORMULAS: SHOW ALL WORK
USING METHODS TAUGHT IN THIS CLASS.
SHOW YOUR GUIDE GRAPH (the graph you are ”bouncing off” of as a dotted
graph.

3. (9 points) Simplify cos(arctan(− 7
x2

)). Show all your work and draw all appropriate triangles.
Your triangle should not have fractions in any of the coordinates/sides. You must
show your work and answer using triangles (DO NOT look up a simplification formula).

4. (6 points) Use a sum/difference identity to find the exact value of cos(105◦).
Do not use reference angles i.e do not calculate cos 75◦

You should be able to do this with only a sum/difference identity and standard angles.
No Decimal Approximations.

5. (9 points) The terminal side of an angle θ in standard position is given by 2x−3y = 0; x ≤ 0.
Sketch the least positive angle theta and then find sin θ.
Rationalize denominators when appropriate.

6. (9 points) Find the exact value (no decimal approximations) of cos θ given that sin θ = −2
3

and θ is in quadrant III. Show all work and draw all appropriate triangles.

7. (12 points) Solve each triangle that exists for C = 52.33◦, a = 79.86ft and c = 72.55ft.
Show all of your work solving your equations. Round to 2 decimals.

8. (11 points). Use vectors to solve this problem (do not use the law of cosines). A ship
leaves port on a bearing of S34.1◦E and travels a distance of 11.9km. The ship then turns
due west and travels 4.7km and then turns north and travels 2.5km. How far is the ship from
port? Round your answer to 2 decimals.

9. (16 points) Solve the following equations over [0, 2π).

(a) 2 sinx tanx = tanx

(b) secx+ tanx = −3 (Use the squaring method. Do not change into sines and cosines.)

10. (10 points) A student is solving the following equation for x (in radians):
sin 2x = A (where A is some number between −1 and 0).

A is not on the unit circle so the student solves by using inverse sine on their calculator and
types in sin−1A into their calculator and gives that as their answer. Is this the correct answer?
If not, what did the student do wrong and how can they fix it? Explain using words, pictures,
and equations.