7.2 VERIFYING TRIGONOMETRIC IDENTITIESBy the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

PROOFS OF TRIGONOMETRIC IDENTITIES Transform the more complicated side into

the more simple side. (This is what we did in example 3 for 7.1)

You are ONLY allowed to work on one side of the equation.

Use the basic trig functions, and , as much as possible.

Factor or multiply to simplify. Use Multiply by the equivalent of 1. Add 0, Watch for Pythagorean identities… all of them

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

PYTHAGOREAN IDENTITIES

…

… All of the Pythagorean identities have a square in

them…look for that!

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

Given

Reciprocal ID

Reduce

Pythagorean identity

Steps Justifications

A.

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

Given

Common factor

Pythagorean identity

Reciprocal identity

reduce

Steps Justifications

B.

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

Given Pythagorean

identity Reduce num/den

Rewrite

Reciprocal identities

Quotient identity

Steps Justifications

C.

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

Given

Reduce num/den

Reciprocal property

Steps Justifications

D.

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

??? WHAT????We want , so lets get it

Given Reciprocal

property Simplify Pythagorean

identity Add 0 Pythagorean

identity

Steps Justifications

E.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

Given Distributive property

(FOIL, etc) Reciprocal property Quotient property Sum to 0 Simplify Combine fractions Pythagorean ID Reduce num/den

Steps JustificationsF.

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

EXAMPLE 1: VERIFY THE TRIG IDENTITY

Given Pythagorean

identity Distributive

property Reciprocal identity Quotient identity

Steps JustificationsG.

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

SUMMARY1. What is the next step in the proof of

2. Using the fact that , show that

*hint: how can I get 2 ’s on the left side?

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

SUMMARY1. What is the next step in the proof of

2. Using the fact that , show that

*hint: how can I get 2 ’s on the left side?

By the end of the period students will use the basic trig identities to verify other trig identities, as evidenced by completion of a collaborative poster.

PARTNER POSTER As a pair, put the steps of your trigonometric

proof in order. For each step determine which basic trig

identity was used and write that in the justification side of the proof

Create a poster to display your work. NEAT and Legible Use of color for clarity