Derivation_Project_BGW

Derivation_Project_BGW - Mahoney Project Due MAC1114 –...

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Unformatted text preview: Mahoney Project Due April 19, 2011 MAC1114 – Spring 2011 – UF Name: _____________________________ Per: 2 3 7 UF ID: ___ ___ ___ ___ – ___ ___ ___ ___ Page 1 of 16 Mr. Mahoney wanted to go over the derivation of several fundamental identities in class but just does not have enough time to do that. The following H.W. Project is Due April 19, 2011 will guide you through the process of doing several of these derivations. Complete the following… Sign the Honor Statement: "On my honor, I have neither given nor received unauthorized aid in doing this assignment." Signature: ________________________________________ Copy the Weird Sentence Below using your usual handwriting: "The quick brown fox tries to jump over a lazy dog.” Sentence: ____________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Copy the Number: "9,034,761,852” Number: _____________________________________________________________________________ You may work alone , with friends , or even with tutors as long as you long as you turn in a copy of this assignment with your work on it . The Assignment must be turned in stabled with this page completed and your name on it. In this project we will derive and explore the following identities: cosgG + ¡¢ = cos G cos ¡ − sin G sin ¡ cosgG − ¡¢ = cos G cos ¡ + sin G sin ¡ singG + ¡¢ = sinG cos ¡ + cosG sin ¡ singG − ¡¢ = sinG cos ¡ − cosG sin ¡ sin £ ¤ 2 − ¥¦ = cos¥ cos £ ¤ 2 − ¥¦ = sin¥ sinG § = sin ¡ ¨ = sin ¥ © ª « = ¬ « + ­ « − 2¬­ ⋅ cos§ ¬ « = ª « + ­ « − 2ª­ ⋅ cos¨ ­ « = ª « + ¬ « − 2ª¬ ⋅ cos © Mahoney Project Due April 19, 2011 MAC1114 – Spring 2011 – UF Name: _____________________________ Per: 2 3 7 UF ID: ___ ___ ___ ___ – ___ ___ ___ ___ Page 2 of 16 The Derivation of gG¡¢£ + ¤¥ . Let ¦ and § be arbitrary angles (that means they can be anything ). The following diagram shows the unit circle with several angles, rays, terminal points, and line segments outlined. Do: In the following observations circle or underline the correct choice to make the observation true. Observe: The angle ¦ [ is / is not ] in standard position and its amount of rotation is labeled with the color red . Observe: The angle – § [ is / is not ] in standard position and its amount of rotation is labeled with the color blue . Observe: The angle ¤ [ is / is not ] in standard position and its amount of rotation is also labeled with the color blue ....
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Derivation_Project_BGW - Mahoney Project Due MAC1114 –...

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