Welcome to Unit 7! HW: 1 ) HW #1: p 427 # ) Make a stamp sheet OR print it out from my website Update: I will have your Unit tests graded by Thursday/ Friday If you have not taken the test yet, please come see me. Please note: I will not be here on Wednesday.

Agenda 1.Pass Back Old Quizzes 1.7.1: Basic Identities 2.Investigation! 3.Finish 7.1 Notes 4.Round Robin

Learning Objectives By the end of this period you will be able to:  Identify and use reciprocal, quotient, Pythagorean, and opposite-angle identities to find trigonometric values.

Many sunglasses have polarized lenses that reduce the intensity of light. When unpolarized light passes through a polarized lens, the intensity of the light is cut in half. If the light passes through another polarized lens with its axis at an angle of θ to the first, the intensity of the light is again diminished.

Th e intensity of the emerging light can be found using the formula I = I 0 – (I 0 / csc 2 θ) I 0 is the intensity of light incoming to the second polarized lens I is the intensity of the emerging light θ is the angle between the axes of polarization Simplify the formula. Can you get all the I 0 ’s together?

Therefore, I 0 – (I 0 / csc 2 θ) = I 0 (1 – sin 2 θ). This is an example of an identity!

7.1 Basic Trigonometric Identities Identity o A statement of equality between two expressions that is true for ALL values of the variable(s). o Example: x 2 – y 2 = (x – y)(x – y) Note: We are specifically covering trigonometric identities (identities that involve trig.)

7.1 Basic Trigonometric Identities Let’s do 1 (a) and you can do 1(b)!

7.1 Basic Trigonometric Identities Reciprocal Identities On one whiteboard work with your table partners to predict what the reciprocal identities could be.

7.1 Basic Trigonometric Identities Quotient Identities On one whiteboard work with your shoulder partner to predict what the quotient identities could be. Hint: This is how you get tan and cot.

7.1 Basic Trigonometric Identities Take 8 minutes to complete the Investigation on the back of your notes to find the Pythagorean Identities. Recall: What is the Pythagorean Theorem? You may have to apply the reciprocal and quotient identities. For 1 (a) and (b) state it in terms of sine, cosine, or tangent.

7.1 Basic Trigonometric Identities Pythagorean Identities 1 ( c) 1( d ) 1( e )

7.1 Basic Trigonometric Identities

Whiteboards!

7.1 Basic Trigonometric Identities Write these notes on the bottom of your investigation. Opposite-Angle Identities

7.1 Basic Trigonometric Identities Write these notes on the bottom of your investigation. Example 3: ( Preview to Tuesday/Wednesday’s Lesson) Prove each trig identity. 1 – cot θ = 1 + cot( – θ)

Round Robin Put your notes away and take out ONE whiteboard per table. Today you have learned a total of 14 identities! Without looking at your notes, you are going to go around the table and list one identity that you learned and then pass the whiteboard around the table. Continue doing this until you and your table have written down ALL 14 identities. If you are stuck on your turn, you may ask your table- mates but try to do this without asking for help!