Secondary Mathematics III

Strand: FUNCTIONS - Trigonometric Functions (F.TF)

Extend the domain of trigonometric functions using the unit circle (Standards F.TF.1–3). Model periodic phenomena with trigonometric functions (Standards F.TF.5–7).

Standard F.TF.3

Use special triangles to determine geometrically the values of sine, cosine, tangent for Π/3, Π/4 and Π6, and use the unit circle to express the values of sine, cosine, and tangent for Π – x, Π + x, and 2Π – x in terms of their values for x, where x is any real number.

• Equilateral triangles and trigonometric functions
The purpose of this task is to apply knowledge about triangles to calculate the sine and cosine of 30 and 60 degrees.
• Foxes and Rabbits 2
The example of rabbits and foxes was introduced to illustrate two functions of time given in a table. We are now in a position to actually model the data given previously with trigonometric functions and investigate the behavior of this predator-prey situation.
• Foxes and Rabbits 3
The example of rabbits and foxes was introduced to illustrate two functions of time given in a table. The same situation was used in F-TF Foxes and Rabbits 2 to find trigonometric functions modeling the data in the table. The previous situation was somewhat unrealistic since we were able to find functions that fit the data perfectly. In this task, on the other hand, we do some legitimate modelling, in that we come up with functions that approximate the data well, but do not perfectly match, the given data.
• FUNCTIONS - Trigonometric Functions (F.TF) - Sec Math III Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics III - Trigonometric Functions (F.TF).
• Introduction to the Materials (Math 3)
Introduction to the Materials in the Mathematics Three of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• Module 7: Trig. Functions, Equations & Identities - Student Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 7, Trigonometric Functions, Equations, and Identities, students work with more trigonometric graphs, beginning with the familiar Ferris wheel context.
• Module 7: Trig. Functions, Equations & Identities - Teacher Edition (Math 3)
The Mathematics Vision Project, Secondary Math Three Module 7, Trigonometric Functions, Equations, and Identities, students work with more trigonometric graphs, beginning with the familiar Ferris wheel context.
• Representing Trigonometric Functions - Ferris Wheel
This lesson unit is intended to help educators assess how well students are able to model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions, and interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.
• Special Triangles 1
Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, we can derive the sine and cosine of special angles, in this case of Ï€/4. This task can be done as a mini lecture soliciting responses from the students, or as a challenge problem for students to ponder and discuss.
• Special Triangles 2
Using known facts about the unit circle and isosceles triangles together with the Pythagorean Theorem, we can derive the sine and cosine of special angels, in this case of Ï€/6. This task can be done as a mini lecture soliciting responses from the students, or as a challenge problem for students to ponder and discuss.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.