 Secondary Mathematics II

Strand: FUNCTIONS - Trigonometric Functions (F.TF)

Prove and apply trigonometric identities. Limit θ to angles between 0 and 90 degrees. Connect with the Pythagorean Theorem and the distance formula (Standard F.TF.8).

Standard F.TF.8

Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

• Calculations with sine and cosine
The goal of this task is to study some values of sinx and cosx looking for and then explaining patterns.
• Finding Trig Values
This is a very straight forward task that addresses the second part of F-TF.C.8 exactly. It could be used as an introductory example, practice or assessment.
• FUNCTIONS - Trigonometric Functions (F.TF) - Sec Math II Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Trigonometric Functions (F.TF).
• Introduction to the Materials (Math 2)
Introduction to the Materials in the Mathematics Two 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 6: Similarity & Right Triangle Trigonometry - Student Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 6, Similarity and Right Triangle Trigonometry, introduces the last of the transformations, dilation. A big idea of Module 6 is that two figures are similar if a sequence of rigid transformation and dilations exists that maps one figure onto the other.
• Module 6: Similarity & Right Triangle Trigonometry - Teacher Edition (Math 2)
The Mathematics Vision Project, Secondary Math Two Module 6, Similarity and Right Triangle Trigonometry, introduces the last of the transformations, dilation. A big idea of Module 6 is that two figures are similar if a sequence of rigid transformation and dilations exists that maps one figure onto the other.
• Trigonometric Ratios and the Pythagorean Theorem
The purpose of this task is to use the Pythagorean Theorem to establish the fundamental trigonometric identity sin2θ+cos2θ=1 for an acute angle θ. The reasoning behind this identity is then applied to calculate cosθ for a given obtuse angle. In order to successfully complete part (c) students must be familiar with the definitions of trigonometric functions for arbitrary angles using the unit circle (F-TF.2). 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.

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