Precalculus Second Semester Final Review focuses on essential trigonometry concepts and problem-solving techniques. It includes exercises on sine, cosine, tangent, and their inverses, as well as applications involving angles and triangles. Students will find practice problems related to the Law of Sines and Law of Cosines, along with graphing trigonometric functions. This review is ideal for high school students preparing for final exams in precalculus courses. Key topics covered include angle conversions, trigonometric identities, and limits.

Key Points

  • Includes practice problems on sine, cosine, and tangent functions.
  • Covers Law of Sines and Law of Cosines for triangle calculations.
  • Features exercises on converting between degrees and radians.
  • Provides a comprehensive review of trigonometric identities and equations.
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11 pages
Exams
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11 pages
Exams
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Precalculus Second Semester Final Review
This packet will prepare you for your second semester final exam. You will find a
formula sheet on the back page; these are the same formulas you will receive for
your final exam. This packet, as well as the final, should be completed using a
scientific calculator only
.
Chapter 4A Trigonometry
1. Refer to . Find
a.  __________
b.  __________
c.  __________
d.  __________
e.  __________
f.  __________
2. Find DE and EF to the nearest hundredth.
DE = __________
EF = __________
3. A flagpole casts a shadow 50 feet long
when the elevation of the sun is 25
°
. How
tall is the flag pole?
4. Convert to degrees without using a calculator.
radians
5. Convert to
exact
radians without using a calculator.
135
°
Give the
exact
value.
6. 
7. 
°
8. 
°
9. 

10. 

11. 
12. Find all values of between 0 and 2 such that 
.
13. Find two values of between 0 and 2 such that 
.
14. If 
and 0
, find 
Chapter 4B Graphs of Trig Functions
Evaluate without a calculator. Give an
exact
answer in radians.
15. 

󰇡
󰇢
16. 󰇡
󰇢
17. 

󰇡
󰇢
18. 

󰇡
󰇢
19. 

󰇛
󰇜
20. Complete the following table:
f(
) =

g(
) =

h(
) =

Domain
Range
Zeros
Period
Give a) the period and b) the amplitude of each function.
21.
y
= 
a)_________________ b)______________________
22.  a)_________________ b)______________________
Sketch one cycle of the graph without using a graphing device.
23. 
24. 
25. Multiple Choice. Which is the equation that corresponds to the following graph?
(a)  
(b) 
(c) 
(d)

Match each equation with its graph below. (HINT: Solve for
y
1
st
!!)
26.

_______
27.   ______
28.  

______
29.  
______
30.
 ______
31.
y
2
sin
2
 _____
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FAQs

What types of problems are included in the trigonometry review?
The review includes a variety of problems focusing on trigonometric functions such as sine, cosine, and tangent. Students will encounter exercises that require them to find values of these functions for given angles, as well as problems that involve real-world applications, such as calculating heights using shadows and angles of elevation. Additionally, there are problems related to the Law of Sines and Law of Cosines, which are essential for solving triangles.

How does the review help with angle conversions?
The review provides specific exercises that guide students through converting angles from radians to degrees and vice versa. For example, it includes problems that require converting π/5 radians to degrees, ensuring that students understand the relationship between these two measurement systems. Mastery of angle conversions is crucial for solving trigonometric equations and understanding the unit circle.

What is the significance of trigonometric identities in this review?
Trigonometric identities are fundamental tools in precalculus that allow students to simplify expressions and solve equations. The review emphasizes key identities such as the Pythagorean identities, reciprocal identities, and angle sum and difference formulas. Understanding these identities enables students to manipulate trigonometric expressions effectively, which is essential for higher-level mathematics and calculus.

What graphing concepts are covered in the review?
The review includes sections on graphing trigonometric functions, focusing on their periodic nature, amplitude, and phase shifts. Students will learn how to sketch graphs of sine and cosine functions, as well as transformations that affect their shapes. Understanding these concepts is vital for visualizing trigonometric functions and analyzing their behavior over different intervals.

How does the review prepare students for final exams?
This review is designed to consolidate knowledge and skills acquired throughout the precalculus course, making it an effective study tool for final exams. By working through a variety of problems, students can identify areas of strength and weakness, allowing them to focus their study efforts accordingly. The comprehensive nature of the review ensures that students are well-prepared for the types of questions they may encounter on their exams.