Simplifying Trig Identities answers.notebook

1

November 26, 2012

Oct 302:59 PM

MATH 301

UNIT 7

Trigonometry 3IDENTITIES

http://ioanemath.wikispaces.com/PreCalculus http://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=KzYWOKLF3vFM:&imgrefurl=http://www.nerdytshirt.com/trigonometrytshirts.html&docid=3ecxKiRuYHSp1M&imgurl=http://www.nerdytshirt.com/images/shirtimages/trigonometry/fakeidtshirt43b.jpg&w=261&h=284&ei=GUKQULH8CcTW2gX6moHYBg&zoom=1&iact=hc&vpx=836&vpy=287&dur=404&hovh=165&hovw=152&tx=140&ty=112&sig=109971733282591085494&page=1&tbnh=147&tbnw=135&start=0&ndsp=17&ved=1t:429,i:92

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Oct 312:50 PM

LESSON 1Simplifying Trigonometric Expressions

OUTCOME:

Simplify trigonometric identities, using::  Reciprocal identities:  Quotient identities:  Pythagorean itentities

http://ioanemath.wikispaces.com/pre-calculushttp://www.google.ca/imgres?hl=en&safe=active&authuser=0&biw=1280&bih=675&tbm=isch&tbnid=-kzywok-lf3vfm:&imgrefurl=http://www.nerdytshirt.com/trigonometry-tshirts.html&docid=3ecxkiruyhsp1m&imgurl=http://www.nerdytshirt.com/images/shirt-images/trigonometry/fake-id-t-shirt-43b.jpg&w=261&h=284&ei=gukqulh8cctw2gx6mohybg&zoom=1&iact=hc&vpx=836&vpy=287&dur=404&hovh=165&hovw=152&tx=140&ty=112&sig=109971733282591085494&page=1&tbnh=147&tbnw=135&start=0&ndsp=17&ved=1t:429,i:92http://www.nerdytshirt.com/get-a-tan.html

Simplifying Trig Identities answers.notebook

2

November 26, 2012

Oct 313:27 PM

In mathematics it is important to understand the difference between an equation

and an identity.

2x  3 = 9  is an equation.  It is only true for the value x = 6.

3x + 5x = 8x is an identity.  It works for all values of x.

Try plugging in any value of x.Does it hold true?

A trigonometric identity is a trigonometric equation that is true for all permissible values of the variable in the expressions on both sides of the equation.

Introduction to Trigonometric Identities

Nov 2211:29 AM

These are all on the formula sheet.

Simplifying Trig Identities answers.notebook

3

November 26, 2012

Nov 2410:43 PM

Pythagorean Identities: Where do they come from?

x2 + y2 = r2 1.  Divide every term by r2.

Nov 111:02 AM

Verification:

Verify the following identies for the given value:a) b)

*  Does this prove that these identities are true for all values of x?

*  Graph each equation with LS in y1, and RS in y2.  What do you notice?  Does this   prove the identity for all values of x?

*  In lesson 2 you will learn how to prove an identity for ALL values of x.   

the substitution of a value in place of x to show one side of an identity equals another.

Simplifying Trig Identities answers.notebook

4

November 26, 2012

Nov 2411:04 PM

Simplifying Trig Expressions

KEY to Simplification:

Express everything in terms of sine and/or cosine first.  

Nov 2211:32 AM

Identities can be used to simplify trigonometric expressions.

Simplifying Trig Identities answers.notebook

5

November 26, 2012

Nov 2211:34 AM

(1 + tan x)2  2 sin x sec x

Nov 12:37 PM

Simplifying Trig Identities answers.notebook

6

November 26, 2012

Nov 12:43 PM

Factor the following trigonometric expressions.  Write in simplest form.

a) b)

Nov 12:41 PM

Express        in terms of sin A and Cos A and write 

in simplest form. 

Simplifying Trig Identities answers.notebook

7

November 26, 2012

Nov 2211:36 AM

Summary: 

Nov 12:47 PM

1.Pg 296 #14

2. TRIG3 L1 Assignment.docx

TRIG 3

Lesson 1

ASSIGNMENT

1.Verify the following identities for the given value of the variable.

a) for b) for

c) for

2.Use identities on your formula sheet to state whether the following are true or false.

a)b)

c)d)

e)

3.Factor each of the following to write it in simpler form.

a)b)

c)d)

4

p

q

=

22

1cotcsc

xx

+=

6

x

p

=

22

cos1sin

xx

=+

(sin)(csc)1

xx

=

2

sin1cos

xx

=-

(tan)(cot)1

xx

=

22

tansec1

xx

-=

2

secsinsec

xxx

-

44

sincos

xx

-

2

2

sinsincos

sin

xxx

x

-

2

sincossin

cos1

xxx

x

-

-

cos

cot

sin

x

x

x

=

3

x

p

=

22

cossin1

qq

+=

SMART Notebook

Attachments

TRIG3 L1 Assignment.docx

TRIG 3

Lesson 1

ASSIGNMENT

1.Verify the following identities for the given value of the variable.

a) for b) for

c) for

2.Use identities on your formula sheet to state whether the following are true or false.

a)b)

c)d)

e)

3.Factor each of the following to write it in simpler form.

a)b)

c)d)

4

p

q

=

22

1cotcsc

xx

+=

6

x

p

=

22

cos1sin

xx

=+

(sin)(csc)1

xx

=

2

sin1cos

xx

=-

(tan)(cot)1

xx

=

22

tansec1

xx

-=

2

secsinsec

xxx

-

44

sincos

xx

-

2

2

sinsincos

sin

xxx

x

-

2

sincossin

cos1

xxx

x

-

-

cos

cot

sin

x

x

x

=

3

x

p

=

22

cossin1

qq

+=

SMART Notebook

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Attachments Page 1