Mastering MAC 1114: Trigonometry at UF

Why MAC 1114 Matters (And Where It Can Trip You Up)

MAC 1114—Trigonometry—is a focused 2-credit course at the University of Florida that builds on algebra and prepares you for calculus. You’ll work with the unit circle, the six trig functions and their graphs, identities, inverse trig functions, and applications. For many students it’s the first time “angle” and “ratio” turn into functions with period, amplitude, and phase shift—and the unit circle can feel like a wall of memorization. I'm a UF alumnus and I teach and tutor math now; this guide is for both students in the class and parents who want to support them. It answers the questions I hear most and gives you concrete ways to study, when to get help, and where to find it.

Is Trigonometry at UF Really That Hard?

Parent: My student did okay in algebra. Should we expect trig to be a big step up, or is it manageable?

Student: I’ve heard the unit circle is brutal. Is that true?

It depends on your background, but MAC 1114 is very manageable with consistent practice. The course is compact: you go from right-triangle definitions to the unit circle, then to graphing $\sin$ , $\cos$ , $\tan$ and their transformations, then identities and equations. The students who do well usually get the unit circle down early (at least the first quadrant and the sign pattern by quadrant), practice “which identity?” before exams, and don’t wait until the night before to get help. The unit circle becomes less brutal once you see the patterns; targeted practice and a few focused sessions make a real difference.

What MAC 1114 Actually Covers

MAC 1114 is typically 2 credits. Prerequisites are usually college algebra (e.g. MAC 1105) or equivalent; check UF’s current requirements. Syllabi vary by instructor, but the core is fairly consistent:

Right triangles and the unit circle — definitions of $\sin$ , $\cos$ , $\tan$ (and csc, sec, cot) in terms of sides and on the unit circle; special angles; reference angles.
Graphs of trig functions — $y = \sin x$ , $\cos x$ , $\tan x$ and their transformations: amplitude, period, phase shift, vertical shift. Connecting formula to graph shape.
Trigonometric identities — Pythagorean identities, sum/difference, double-angle, half-angle; verifying identities and using them to simplify or solve.
Trigonometric equations — solving equations involving trig functions (often using identities or substitution); general solutions vs restricted intervals.
Inverse trig functions — definitions, domains and ranges, and solving equations like $\sin^{-1}(x) = \theta$ .
Applications — right-triangle applications, simple periodic models, and sometimes exponential/log in an analytic context.

At UF, Exam 1 often hits the unit circle, basic graphs, and maybe the start of identities; Exam 2 hits identities, equations, and inverse trig. Nailing the unit circle and “what does the graph look like?” early sets you up for the rest.

When Are the Exams? When’s the Best Time to Get Help?

Parent: When do they usually have exams? I’d like to suggest getting a tutor before the first one, not after a bad grade.

Student: I’m already lost. Is it too late to get help before the final?

Typical structure (always confirm with your syllabus): two or three midterms plus a final. Best times to get help:

Before Exam 1: Focus on the unit circle (values at special angles, signs by quadrant) and the graphs of $\sin$ , $\cos$ , $\tan$ and basic transformations. One or two focused sessions can make the first exam feel much more manageable.
Before Exam 2: This is where identities and trig equations pile up. Get clear on “which identity do I use?” and on solving equations (factoring, substitution, general solution). Catching up here prevents the second half from feeling overwhelming.
Before the final: The final is often cumulative. Prioritize unit circle, graphing (amplitude, period, phase shift), key identities, and solving equations. It’s not too late—a lot of students I work with do a short final-prep block and still improve a lot.

Where Students Get Stuck

The unit circle: “I don’t know how to remember all of it”

You don’t have to memorize every angle—focus on the pattern. Know the first quadrant (0°, 30°, 45°, 60°, 90° and their radian equivalents and coordinates). For other quadrants, use reference angles and the sign of $x$ and $y$ (cos and sin). Practice “what is $\sin(5\pi/6)$ ?” and “what angle in $[0, 2\pi)$ has $\cos \theta = -1/2$ ?” until it’s automatic. Once the unit circle clicks, the rest of the course builds on it.

Graphing: amplitude, period, phase shift

For $y = A \sin(Bx - C) + D$ : $|A|$ = amplitude, $2\pi/|B|$ = period, $C/B$ = phase shift (right if positive), $D$ = vertical shift. Draw one period first, then extend. Desmos is great for checking: type the function and compare to your sketch.

Identities: “I don’t know which one to use”

Start with the Pythagorean identities ( $\sin^2\theta + \cos^2\theta = 1$ and the ones for $\tan^2$ and the others) and the definitions in terms of $\sin$ and $\cos$ . For verifying or simplifying, try rewriting everything in terms of $\sin$ and $\cos$ , or look for a pattern (sum/difference, double-angle). Practice a few “verify this identity” and “simplify this expression” problems; the patterns repeat.

Solving trig equations

Get one trig function (or a single angle) if you can—use identities or substitution. Then solve for the angle (remember general solution: $\theta + 2\pi k$ for sine/cosine, $\theta + \pi k$ for tangent) and plug back into the original variable if you substituted. Check your syllabus for whether your instructor wants general solution or solutions in a given interval.

Inverse trig: domain and range

$\sin^{-1}(x)$ returns an angle in $[-\pi/2, \pi/2]$ ; $\cos^{-1}(x)$ in $[0, \pi]$ ; $\tan^{-1}(x)$ in $(-\pi/2, \pi/2)$ . Know those ranges so you give the correct angle when solving equations or simplifying.

Can They Still Pass If They’re Already Behind?

Parent: My student bombed the first exam. Is it still possible to pass?

Student: I’m failing right now. What do I do?

Yes. Grades are usually weighted (e.g. midterms 50%, final 30%, homework 20%—check your syllabus). That means:

The final often counts a lot and is cumulative. Doing well on it can pull up a low midterm.
Homework is “free” points if you do it; don’t skip it.
Dropped lowest quiz or similar policies can help—use them.

The key is to stop guessing and start targeting. Figure out the 2–3 topics that show up most on past exams (often unit circle, graphing, identities, solving equations) and focus there. One or two tutoring sessions focused on those can turn confusion into a clear process. Catching up is very possible; waiting until the last week is not ideal but still worth doing.

Study Strategies That Work

Do homework the same day (or next day) the material is covered. Letting it pile up makes the unit circle and identities feel impossible.
Go to office hours with specific questions (“I don’t get when to use the double-angle identity”) and one or two problems you attempted.
Practice the unit circle until you can quickly give $\sin$ , $\cos$ , $\tan$ at special angles and in each quadrant. Then practice “sketch one period of this function” and “solve this equation.”
Use past exams if your instructor posts them. They show what’s really emphasized (often graphing, identities, and solving equations).
Use free online resources. Khan Academy – Trigonometry is topic-by-topic and free; Desmos is ideal for checking trig graphs. We don’t have trigonometry notes on the site yet—targeted tutoring plus these resources works well.
Form a study group and take turns explaining the unit circle or verifying an identity. Teaching someone else forces you to understand.

Key Resources for MAC 1114 at UF

Online (start here)

We don’t have a trigonometry course on the site yet. Until then, these free resources are the best place to reinforce lecture and practice:

Khan Academy – Trigonometry — unit circle, trig functions, identities, equations. Use it alongside your class: after a lecture, do the corresponding unit and a few exercises.
Desmos Graphing Calculator — type in $\sin$ , $\cos$ , $\tan$ and see graphs; play with amplitude, period, and phase shift. Use it to check your work and build intuition.
The Organic Chemistry Tutor – Trigonometry Playlist — clear video walkthroughs when you need a second explanation.

At UF

UF Math Department — course info, sometimes past syllabi.
Broward Teaching Center — tutoring and study support.
UF Libraries Course Reserves — your textbook and sometimes solution manuals or extra materials.

Books

Dugopolski’s Trigonometry and Stewart/Redlin/Watson’s Algebra and Trigonometry (or Precalculus: Mathematics for Calculus) are common at UF; the examples align with what you’ll see in 1114.

How I Tutor MAC 1114

I’m a UF alumnus (MS in Electrical and Computer Engineering) and I teach math at Santa Fe College. When students or parents reach out about MAC 1114, we usually focus on:

Unit circle fluency — special angles, signs by quadrant, and “what is $\sin(\theta)$ ?” so you’re not guessing on exam problems.
Graphing — amplitude, period, phase shift, and connecting formula to graph so you can sketch and interpret.
Identities — which identity when, and practice verifying and simplifying until the patterns stick.
Solving trig equations — setting up the equation, using identities, and writing general solutions or solutions in an interval.
Connecting the math to your class so you’re ready for your professor’s exams and wording.

Sessions are online, and we tailor them to where you are: catching up after a bad exam, prepping for the final, or staying ahead week by week. A lot of students do a few sessions before Exam 1 and again before Exam 2; others prefer regular weekly sessions. Either way, the goal is to make the material clear and to give you a process you can use on your own.

What Students Say After Getting Targeted Help

"I was traveling the weekend before a precalc test and really needed help with trigonometry. Zachary was available on short notice and helped me better understand several concepts. After our sessions, I felt much more confident in my ability to do well on my exam. Zachary truly was a lifesaver!" — UF Student

"Zachary really knows his stuff! He has helped me so much with my calculus. Very helpful and patient. Well versed and knowledgeable. He has really helped me level up my skills." — Michelle G., Calculus 1

"Zachary is very knowledgeable, patient, and understanding. I would recommend anybody who is struggling with calculus. Calculus is not an easy subject so it's nice to find a tutor who understands what you are going through." — Marjorie S., Calculus

Bottom Line

MAC 1114 at UF is trigonometry in a compact package: unit circle, trig functions and graphs, identities, equations, and inverse trig. Stay on top of homework, get the unit circle and graphing down before Exam 2, and don’t wait until the night before an exam to get help. Use office hours, free online resources (Khan Academy, Desmos), your textbook, and—if you want someone who knows the course and can tailor sessions to your syllabus—targeted tutoring. Whether you’re preparing for the first exam or the final, focusing on the right topics and having a clear process makes a real difference.

If you’re a UF student (or the parent of one) and you want that kind of focused support for MAC 1114, you can schedule a session here. I work with Gators every semester and would be glad to help you or your student get through Trigonometry with confidence.