Trigonometry and Periodic Functions of Alg 2 (#1 of 2)

Trigonometry is one of my favorite topics to teach, and unit circle and graphing skills that you learn in this unit will help you to understand further study of trigonometry. Students looking for a head start or review of angles of rotation, the unit circle, and graphs of trigonometric identities will enjoy this course. After completing this unit, you will be very well prepared to continue your study in the following class: Triangle Trigonometry, Identities, & Equations of Algebra 2.

The phases of the moon, the corresponding high and low tides of the ocean, the data given in an electrocardiogram (EKG), and sound waves can all be described in terms of cycles (or periods). One important study of trigonometry is its cyclic nature and how that can be applied in the real world. In this unit, the first of two units that encompass the Trigonometry of Algebra 2, you will study periodic data, angles of rotation, arc length, the unit circle, radian and degree measure, evaluating all six trig functions in a variety of ways, and sketching graphs of all six trig functions. 

We will move rather quickly in this unit. Students with a firm Algebra 1 background, the ability to work at the Algebra 2 level, and a dedication to working hard and learning something new should do well in this unit course.

Course Syllabus:
Day 1 - Sketch angles in standard position. Name coterminal and reference angles. Define radian measure. Solve for radian measure of an angle, radius of the circle, or arc length depending on information given. Convert between radian and degree measure.
Day 2 - Define six trig functions and find exact values of 5 remaining trig functions given one value and the angle’s terminating quadrant or given a point on the terminal side of the angle.
Day 3 - Construct the Unit Circle. Find exact values of cosine, sine, tangent, secant, cosecant, and cotangent of special angles using the Unit Circle. Practice Test #1 and Test #1 will be uploaded at the conclusion of this class session.
Day 4 - Explore periodic functions and state period and amplitude given a graph. Graph the sine and cosine functions and transformations. State the period, amplitude, phase shift, and vertical shift. 
Day 5 - Graph the tangent and cotangent functions and transformations. State the period, phase shift, vertical shift, and asymptotes. Write equations of cosine, sine, tangent, and cotangent functions given defining characteristics.
Day 6 - Graph the secant and cosecant functions and transformations. State the period, phase shift, vertical shift, and asymptotes. Practice Test #2 and Test #2 will be uploaded at the conclusion of this class session.

Students will be asked to complete daily assignments and are welcome, but not required, to submit their work to me for feedback. Answer keys will be provided, daily, for students to self check their work.

Two 100-point tests will be posted to the classroom for students to complete and return to me. Test #1 will be posted at the conclusion of the class session on Day 3 and should be submitted no later than 2 hours before the start of class on Day 4. Test #2 will be posted at the conclusion of Day 6 and should be submitted within 24 hours.

Students will be continually urged to take neat and accurate notes, constantly review those notes, participate in class discussion in order to communicate understanding, follow all notes while completing assignment problems, carefully check each assignment problem with provided solutions, rework each missed assignment problem. This material can be great fun and rewarding. We will affirm and encourage each other, and students are encouraged to communicate with me either in class or through their learner page or the classroom page if they have any further questions.