Plagiarism Video A SEA DEVIL TV production.

http://www.youtube.com/watch?v=VnTPv9PtOoo

Academic IntegrityTrue or False?

1. Plagiarism is the misrepresentation of another’s academic or artistic work as one’s own. 2.One tip to avoid plagiarism is to use someone’s ideas without referencing the source.3. Plagiarism does not include copying another student’s homework with consent. 4. A breach of academic integrity in the upper school will likely result in the offense becoming a part of the student’s permanent record. A first incidence of academic dishonesty (including, but not limited to, copying another's homework, cheating on a test or quiz, or plagiarism) may lead directly to suspension or a warning/probation.5. Incidences of academic dishonesty is not cumulative – once you enter the next grade, it is erased off of your record.6. The school is obligated to report incidents of suspension to colleges, universities, and other educational institutions when they request such information.

November 7, 2011At the end of today, you will be able to verify Trig Identities.

Warm-up:

Name two angles for, θ, if sinθ = -1/2

HW 4.2b: Pg. 309 #33-42, 53, 55

Fundamental Trig Identities

csc

1sin

sec

1cos

sin

1csc

cos

1sec

cot

1tan

tan

1cot

Reciprocal Identities

Quotient Identities

cos

sintan

cot cossin

Pythagorean Identities

sin2θ + cos2θ = 1 1+ tan2θ = sec2θ

1+ cot2θ = csc2θ

Pythagorean Identities

1sincos 22 222 cba 1

22

hyp

opp

hyp

adj

12

2

2

2

hyp

opp

hyp

adj

12

22

hyp

oppadj

Pythagorean Identities

1sincos 22 222 cba

12

22

hyp

oppadj

12

22

c

ba

12

2

c

c

Lesson 4.2bVerifying Trig Identities

Example 1: Verify that sec2θ – tan2θ = 1Use Trig Identities to convert

1

cos2

sin2cos2

1 sin2cos2

cos2cos2

Since, sin2θ + cos2θ = 1 1 - sin2θ = cos2θ

1 = 1 ✔

They have a common denominator, so…

Try HW #37(1 + cosθ)(1 – cosθ) = sin2θ

When you multiply, you will get: 1 – cos2θ because it is a

difference of squares

sin2θ = sin2θ

Usesin2θ + cos2θ = 1✓

Cofunction Identities

)90sin(cos BB )sin(cos CB

Is this true?Show that cos θ = sin (90° – θ)

Take a look at a 30-60-90 triangle 30°

60°

2

1

√3

cos60 sin(90 60 )

1

2sin(30 )

1

21

2✓

Cofunction Identities

sin2

cos

cos2

sin

tan2

cot

cot2

tan

sec2

csc

csc2

sec

Negative Angle Identities

)tan()tan(

)cos()cos(

)sin()sin(

Add to HW: Show that these identities are true.

Even Function