UGA Trio UB/UBMS Precalculus 6-23-2025
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Class Notes
PDF (not cleaned up) for 6-23
PDF (cleaned up) for 6-24
Homework Problems
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Convert the following angle measures from degrees to radians:
(a) $20^\circ$
(b) $-70^\circ$
(c) $100^\circ$ [/bluebox]
[solution] (a) $\pi/9$
(b) $7\pi/18$
(c) $5\pi/9$
[/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Convert the following angle measures from radians to degrees:
(a) $7\pi/6$
(b) $4\pi/3$
(c) $-13\pi/12$ [/bluebox]
[solution] (a) $210^\circ$
(b) $240^\circ$
(c) $-195^\circ$
[/solution]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Find two positive angles and two negative angles that are coterminal to $-\pi/4$. [/bluebox]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Find an angle between $0$ and $2\pi$ that is coterminal with $19\pi/6$. [/bluebox]
[bluebox] [bluetitle]Problem %counter%.[/bluetitle]
Find the terminal point $P(x, y)$ on the unit circle determined by the following $\theta$:
(a) $\theta = -5\pi$
(b) $\theta = 3\pi/2$
(c) $\theta = -5\pi/2$
(d) $\theta = 5\pi/6$
(e) $\theta = -3\pi/4$
(f) $\theta = 7\pi/4$
(g) $\theta = 7\pi/6$ [/bluebox]
Project
A significant portion of your grade is built into completing a course project. If you work in a group, you will be required to submit peer evaluations as part of your progress reports. Late progress reports will have points deducted.
- Sign-up form: https://forms.gle/pugDSZCoMoqZ6AbR8
Timeline:
- Progress report (15% of project grade): Due June 27th.
- Progress report (15% of project grade): Due July 2nd.
- Project (70% of project grade): Due July 4th.
The following projects are available:
[bluebox] [bluetitle]Project 1 (Unit Circle Art).[/bluetitle]
Description: Make a detailed, creative rendering of the unit circle that visually explains key values (angles in degrees/radians, sine/cosine coordinates).
- Twist: Incorporate a theme — video games, animals, anime, architecture, etc.
- Deliverable: Infographic with labeled angles and coordinates.
This can be done individually or in groups. [/bluebox]
[bluebox] [bluetitle]Project 2 (Trig Zine or Mini-Book).[/bluetitle]
Description: Students create a small zine (booklet) explaining key trig ideas in their own words with doodles, examples, and jokes. This is a 3-4 student group project. [/bluebox]
[bluebox] [bluetitle]Project 3 (Sunset Angle Modeling).[/bluetitle]
Description: Students estimate the sun’s angle of elevation based on shadow length and trig.
- Extension: Use the results to calculate the height of objects like trees, or fellow students.
- Deliverable: Image + angle calculations + infographic.
This is a 3-4 student group project. [/bluebox]
[bluebox] [bluetitle]Project 4 (Euler’s Formula and Trig).[/bluetitle]
Description: Students will create an infographic that demonstrates how to use Euler’s Formula $e^{i\theta} = \cos\theta + i\sin\theta$ to derive various trig identities. This is a 3-4 student group project but can also be a one person project. [/bluebox]
[bluebox] [bluetitle]Project 5 (Solve Some Problems).[/bluetitle]
Description: Students will be given a few involved problems related to topics in the course, solve them, and produce a formal write-up detailing the solution. This can be done either individually or as a group project. [/bluebox]