SUBJECT: PreCal/Trig  

GRADE: 11-12

UNIT TITLE: Unit 5 Trigonometric Functions (Analysis and Application)

TIME FRAME: 7 weeks (1/5-2/25)

ESSENTIAL QUESTION:  How can the knowledge and skills associated with trigonometric functions, identities, and laws be vital to the solving of real-world problems?

CCSS Standards

Student-Friendly Objectives

Student Learning Experiences/Tasks

Assessment

Vocabulary

Resources: Literary Works/ Websites/ Chapters

F.TF.3  .Use special triangles to determine geometrically the values of sine, cosine,

and tangent for pi/3, pi/4, and pi/6, use the unit circle to express the values of sine, cosine, and tangent for x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

Students will be proficient at calculating unknown side and angle measures of right triangles by utilizing basic trigonometric function relationships.

Use the graphing calculator (technology) in determining sides and angles of acute angles, and perform the same without technology by utilizing special right triangle ratios.

Dailly bellringers, weekly quizzes, tesxtbook problems (Ch4.1, 4.2, 4.3)

Special right triangles, sine, cosine, tangent, degrees, radians, angular motion, acute angle, unit circle, coterminal angle, terminal side

Textbook (Ch4), Graphing Calculator, Internet, Powerpoint, Practice/Cornell Notes, projects, textbook activities

F.TF.9  Prove the addition and subtraction formulas for sine, cosine, and

tangent

and use them to solve problems

Students will be proficient at utilizing the defined relationships of sine, cosine, and tangent respective of the sides of a right triangle in manipulation to prove the respective addition and subtraction formulas.

Use Algebra and basic trigonometric definitions to adjust one side of an equation to equal a given addition or subtraction formula result.

Textbook problems (Ch5.1, 5.2)

Pythagorean Identities, Cofunction Identities, Odd-Even Identities, Sum and Difference Identities

Textbook (Ch5.1, 5.2), Trigonometric Identities and Formulas

G.SRT.9  Derive the formula A = (1/2)ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Students will be proficient in their understanding and justification of the area of a triangle formula from basic Geometry by applying trigonometric skills.

With the use of graph paper and trigonometric formulas, students will explore and support the definition of sine and the basic meaning of square units within a triangle with the aid of square units comprising graphical paper.

Textbook problems (Ch5.2)

Area, perpendicular, hypotenuse, square unit

Textbook (Ch.5.1, 5.2), graph paper, protractor

G.SRT.10  Prove the Law of Sines and the Law of Cosines and use them to solve problems

Students will be proficient in the valid proofs of the Laws of Sines and Cosines by utilizing various trigonometric identities and formulas.  Further, students will master the use of these laws by determining unknown sides and angles of oblique triangles

Students will first experience application of these laws to calculate unknown measures of given oblique triangles.  Then applications will be made to navigation problems to enhance understanding and importance.

Textbook problems (Ch5.5, 5.6)

Law of Sines, Law of Cosines, oblique triangle, included angle

Textbook (Ch5), real-world navigation problems

F.TF.6  Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces)

Students will further hone their skills and demonstrate their proficiency of utilizing the Laws of Sines and Cosines to solve real world problems involving direction and angle of motion resultant distance and proximity.

With and without technology, students will explore the construction of sides of triangles and determine measures of these sides and respective opposite angle with the appropriate formulas as well as support their calculations with graphs and construction tools.

Textbook problems (Ch5.6), problems/Internet

Textbook (Ch.5.5,5.6)

Strand  T.3.PC.6 Define and use reciprocal functions cosecant, secant, and cotangent to solve problems.

Students will become familiar with the inverse functions of the basic functions of sine, cosine and tangent by applying them to find unknown measures of various triangles

Students will investigate the nature of these functions in relation to the unit circle by determining sides and angles.

Textbook problems (Ch5.2, 5.3,5.4).

Inverse trig function, secant, cosecant, cotangent

Textbook (Ch5)