Advanced Mathematics I

Advanced Mathematics I

(secondary)

Selective Unit 5 (S05)

(Trigonometric Identities)

(July 20012)

Unit Statement: Almost every word we use has a synonym, a different word an identical meaning. Almost every trigonometric identity has an equivalent expression. In this unit the student will use trigonometric identities to verify that certain statements are equivalent and to find exact values for angle measures that are not normally committed to memory.

Essential Outcomes: (must be assessed for mastery)

1. The Student Will compare and contrast equations with identities.

2. TSW use the reciprocal, tangent and cotangent identities to find secant, cosecant and cotangent of angles 0, 30, 45, 60, 90 degrees. (14.1)

3. TSW use the reciprocal, tangent and cotangent identities to simplify trigonometric expressions and to verify trigonometric identities. (14.1)

4. TSW use the three Pythagorean identities to simplify trigonometric expressions and to verify trigonometric identities. (14.1)

5. TSW use negative angle identities and cofunction identities to solve trigonometric equations and to verify identities. (14.6)

6. TSW use the angle difference and angle sum identities to solve trigonometric equations, to verify identities and to find exact values of angles. (4.6)

7. TSW use the double angle and half angle identities to find exact values of angles. (14.6)

Introduced and Practiced Outcomes:

The Student Will use angle sum identity to derive each double angle identity

Key terms and concepts:

QSI ADV MATHEMATICS I S05

Identity

domain of validity of an identity

reciprocal identities

Pythagorean identities

negative angle identities

cofunction identities

angle difference identities

angle sum identities

double angle identities

half angle identities

to derive, to verify

QSI ADV MATHEMATICS I S05

Suggested Assessment Tools and Strategies:

Attached Rubric or teacher-generated rubric that assesses ALL Essential Outcomes (TSWs).

Students might use a notebook/journal with a list of the identities.

Suggested Resources:

Textbook: Prentice Hall, Algebra 2, Pearson, ISBN -13: 978-0-13-350043-1, the online version of the textbook can be accessed at https://www.pearsonsuccessnet.com

Solve it! – short exercises in the textbook/also listed in teacher resources online

Practice form G, Practice form K – in teacher resources online

Additional Problems - in teacher resources online

Enrichment activities – in teacher resources online

Technology Links:

Teacher and student resources available through the publisher at https://www.pearsonsuccessnet.com/snpapp/login.do?method=login

EVALUATION RUBRIC FOUND ON FOLLOWING PAGE……………

QSI ADV MATHEMATICS I S05

Suggested Unit Evaluation Rubric - ADV MATH I – S05

· To receive a ‘B’ in the unit a student must demonstrate mastery of all TSWs

· To receive an ‘A’ in the unit a student must demonstrate ‘A’ level mastery on at least 3 of the 5 identified TSWs.

Student name:______Date:______

TSW / ‘A’ LEVEL / ‘B’ LEVEL / Notes
1 compare and contrast equations with identities / Student can verbally explain a difference between an identity and an equation. / Student identifies identities in a given set of equations.
2 use the reciprocal, tangent and cotangent identities to find secant, cosecant and cotangent of angles 0, 30, 45, 60, 90 degrees. / Given graphs, student identifies domain of validity for different identities. / Student evaluates tangent, cotangent, secant and cosecant for the standard angle measurements. / Expecting domains of validy without providing graphs might be too difficult.
3 use the reciprocal, tangent and cotangent identities to simplify trigonometric expressions and to verify trigonometric identities. / Student will solve problems similar to those on pages 900-902.
4 use the three Pythagorean identities to simplify trigonometric expressions and to verify trigonometric identities. / Given one of the Pythagorean identities student can derive the other two identities. / Student will solve problems similar to those on pages 900-902.
5 use negative angle identities and cofunction identities to solve trigonometric equations and to verify identities. / Student can explain why the negative angle and cofunction identities work. / Student will solve problems similar to those on pages 940-942. / Projectiles launched from the same height at 30 degrees have the same range as those launched at 60 degrees. This is a fun investigation with projectile launchers.
Also, derive which angle produces the largest range for a projectile.
6 use the angle difference and angle sum identities to solve trigonometric equations, to verify identities and to find exact values of angles. / Student will solve problems similar to those on pages 940-942.
7 use the double angle and half angle identities to find exact values of angles. / Student derives the double and half angle identities. / Student will solve problems similar to those on pages 947-948. / Students should not be given hints on the derivations.

QSI ADV MATHEMATICS I S05