Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind:

A review of the essential mathematics needed to succeed in calculus.
An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools.
This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course.

This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.

Blast a Buick out of a cannon! Learn about projectile motion by firing various objects. Set the angle, initial speed, and mass. Add air resistance. Make a game out of this simulation by trying to hit a target.

The goal of this task is to use rigid motions to establish some fundamental results about angles made by intersecting lines. Both vertical angles and alternate interior angles are treated.

Unit Description
In this five day unit, students will use trigonometric ratios and their inverses and the Pythagorean Theorem to identify the angle measures and board lengths of a Double Howe Truss. Students will test their understanding by constructing a scaled model of the truss.

The goal of this task is to gather together knowledge and skills from the seventh grade in a context which prepares students for the important eighth grade notion of similarity.

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

These Trigonometry lecture videos coterminal angles, trig functions, quadrantal angles, special acute angles, co-functions, finding theta, reference angles, trig functions, radian measure, arc length, area of a sector, graphing sine and cosine using t-table, amplitude and frequency, phase shift for sine and consine, vertical shift, tangent curve, cotangent transformations, evaluating trig identities, trig expressions, sum and difference for cosine, double and half angle identities, inverse, principal values, solving difficult trig equations, law of cosines, area of a triangle, and vectors and bearing.

Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.

In this Cyberchase video segment, Harry tries to snowboard and learns how to measure and identify many common angles.

A park ranger needs to build a zipline to drop food supplies to her mentor park ranger at the bottom of a gorge. Unfortunately, she does not have the instructions to build the zipline according to the proper specifications. Without directions, she is unsure of the correct angles to attach her zipline to each tree. Additionally, she needs to figure out how to open the chute to drop the food supplies.  Challenge: Create a zip line that will release from her bucket (paper cup) the food supplies (represented by a marble) onto the target (placed 5/8 of the way down the zipline)  before the gear reaches the opposite end of the zip line.