MATH 1300: Calculus I Instructor Notes for “Trigonometry Review”

Background content: This is a review project. No background beyond precalc is needed.

Philosophy behind this project: Many students learn trigonometry initially by memorizing.Thus by the time they have reached Calculus 1, many students have forgotten much of what theyonce knew. This project is intended as a chance for students to review trigonometry and identifythe key concepts that they will need for this course. The first page of this project focuses onevaluating trig and inverse trig functions as well as some trig identities. The rest of the projectpresents real-world problems that require trig to solve. Many of these applications will appear laterin the semester when we discuss related rates and rates of change.

Learning goals:

1. Review the unit circle and trig identities.

2. Review using trig for real-world applications.

Implementation notes:

Intro: It may help to give a brief (5 minutes) review of trig at the beginning of class. Thiscould include the definitions of the trig functions (SOH-CAH-TOA), their inverses, and themain values on the unit circle. On the next page of this document is a sheet of unit circlesthat can help facilitate this review.

Page 1: It is important to keep the students moving through this project so that they get tothe later problems. Do not spend more than 10 minutes on the first page. You could have thestudents work through part (a)’s of problems 1-3, then part (b)’s, etc. so that they attemptsome problems of each type. Problems (2f) and (3f) are of particular import since they requireknowledge of the domains and ranges of the trig functions and their inverses.

Page 2: Problems 5 and 6 requires the students to recall the definitions of the trig functions(SOH-CAH-TOA) and think about a situation that involves an object moving at a constantrate.

Break: Take 5 minutes to summarize what trig knowledge the students must know for exams.This includes the definitions of the trig functions, their inverses, the unit circle, the domainsand ranges of the trig and inverse trig functions, and the Pythagorean identities.

Pages 3-4: It is suggested that the students work through problems 5, 6, 9, and 11 afterattempting the first page. These problems deal with applications that will appear later inthe course when we discuss related rates and rates of change. Encourage students to draw andlabel pictures describing the situation. On the last page is a sheet that might help studentsvisualize problem 11 concerning a stripe on a barber pole. Be sure that students are includingunits in their answers.

Wrap-up: Leave approximate 5-7 minutes for a wrap-up. Discuss the advantages of drawing andlabeling pictures to describe the situations presented in the later problems. Note that we didn’tneed any calculus (in particular derivatives) to solve problems 6 and 9. Ask what might changein the problem that would require knowledge of derivatives. Hopefully, this leads to a discussionabout when the rate of change of something is non-constant.

1

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

GGG

G

GG

G

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

GGG

G

GG

G

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

GGG

G

GG

G

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

(__,__)

GGG

G

GG

G