Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
1
Name _______________________________ Class Block: _______
Exam 2023
Grades
Section I
Section II
Section III
Total Points
/100
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
2
Section I: No Calculator. [50pts]
Answer ALL the following multiple choice problems. Do your work in an organized way so
there can be some partial credit.
1) Given angle ϑ =
a)−
b)
, the reference angle is:
π
3
π
3
c) −
d)
7π
3
5π
3
π
6
2) The period of 𝑦 = 3𝑠𝑖𝑛 (2𝑥) − 1 is
a) 2π
b) π
c) 4π
d) 1
3) 𝑓𝑖𝑛𝑑 𝑠𝑖𝑛2θ =
a)
6
5
b)
24
25
c)
7
25
d)
24
5
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
3
4) Which of the following is the reference angle of − 137°
a) 53°
b) 43°
c) 137°
d) 47°
5) Solve for θ for 0≤θ < 2π if 2𝑠𝑖𝑛θ − 1 = 0
π 11π
a) θ = 6 , 6
b) θ =
c) θ =
d) θ =
π
3
π
6
π
3
,
,
,
2π
3
5π
6
5π
3
6) Answer in degrees: 𝑐𝑜𝑠
a)
b)
c)
d)
3
4
b) −
4
3
c) −
3
4
d)
=
− 45°
135°
135°, 225°
225°, 315°
7) If 𝑠𝑖𝑛θ =
a)
−1 − 2
2
4
3
3
5
, and θ 𝑖𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑞𝑢𝑎𝑑𝑟𝑎𝑛𝑡, then 𝑡𝑎𝑛θ =
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
4
(
2
)
2
8) simplify 𝑡𝑎𝑛 θ + 1 𝑐𝑜𝑠 θ =
a) 1
2
b) 𝑐𝑠𝑐 θ
2
c) 𝑠𝑒𝑐 θ
d) 𝑐𝑜𝑠θ
9) The amplitude of 𝑦 =
a) 2
b) -2
c) 1
d) 3
10)
a)
b)
c)
d)
𝑐𝑠𝑐θ =
3
5
4
5
5
4
5
3
− 2𝑠𝑖𝑛(3𝑥 − 6) + 1 is
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
5
__________________________________________________________________
Section II: No Calculator
Sketch out problems, and show all your work in order to receive full/partial credit.
11) Given the angle ϑ =
7𝛑
3
[5pts]
a) Find both a positive and a negative coterminal angle of ϑ
b) Find the reference angle for ϑ
12) If 𝑐𝑠𝑐𝑥 =
3
2
and 90°≤ x ≤270° find the other five trig functions [5pts]
13) Identify the domain and range of each. [5pts]
−1
𝑦 = 𝑐𝑜𝑠 (𝑥 + 1) − 2
Domain:_________________________ Range ________________
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
6
Solve ONE of the following two short answer problems [5pts]
2
14) Verify the identity:
𝑐𝑠𝑐 θ
2
𝑐𝑜𝑡 θ
2
2
(𝑠𝑖𝑛 θ) = 𝑡𝑎𝑛 θ
15) Verify the identity: 𝑐𝑜𝑠(θ − π) =− 𝑐𝑜𝑠 θ
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
7
Solve ONE of the following short answer problems [10pts]
2
16) Find all possible solutions for x in radians 1 + 2𝑠𝑖𝑛 𝑥 = 2
2
17) Solve for θ if 0≤θ < 360° and 2𝑐𝑜𝑠 θ − 𝑐𝑜𝑠θ = 0
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
8
Solve ONE of the following problems [10pts]:
18) Graph 𝑦 = 𝑠𝑒𝑐 (2𝑥 − π) + 1.
List the important information first and then GRAPH!
Amplitude _____
Period. ______
Vertical shift _____
Horizontal shift_____
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
9
19) Find an equation that represents the given graph:
List the important information first and then write the equation!
Amplitude _____
Period. ______
Vertical shift _____
Horizontal shift_____
Equation _________________________________
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
10
__________________________________________________________________
Section III: Calculator
Sketch out problems, and show all your work in order to receive full/partial credit.
20) Suppose Mr. Wildes is looking out of the window of Upper 3 common room and sees Mrs.
Horst walking on the quad. The angle of depression between Mr. Wildes and Mrs. Horst is 57
and Upper 3 is 50ft above the ground? [10pts]
a. How far away from the base of the brick is Mrs. Horst?
b. How far away from Mr. Wildes is Mrs. Horst?
Extra Credit:
What is Ms. Nongera-Nickerson’s Child’s name? [5pts]
______________________________________________
Hon. Precalculus
Fall Final Exam 2023
Remember to show ALL your work!
11
Reflection:
How has the fall term gone? What do you think you did well? What could you have done better?
What do you want Me to continue to do? What should I change? Is there anything you want Me to
know? Have a great break!!
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