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<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang=""> <body class="calibre"> <p class="calibre1"></p> <p class="calibre1">MATH 1163</p> <p class="calibre1">Precalculus Mathematics</p> <p class="calibre1">Fall 2013</p> <p class="calibre1">Can Solve Identities:</p> <p class="calibre1">A Trigonometric Identity Project</p> <p class="calibre1">You have been asked to use your skills with identities to solve a few trigonometric crimes that have recently occurred in your area. You may work with a partner (one only) if you would like to solve the following five cases. You should compile a report detailing your work for each case. For each case, you should clearly identify and explain all steps involved in your solutions. Your completed report should be presented in a professional manner and submitted directly to Professor Adams no later than 2:00</p> <p class="calibre1">PM on Friday, November 22. Late submissions will not be accepted. The Project is worth a maximum value of 50 points. Good luck on your mission! </p> <p class="calibre1">• Case # 1: The Con Artist</p> <p class="calibre1">You think you have tracked down the con artist csc (x) − cot (x) , </p> <p class="calibre1">but he has hidden his true identity. If you can verify that sin (x)</p> <p class="calibre1">1 + cos (x)</p> <p class="calibre1">is in fact his cover up identity, then you will have finally caught the infamous con artist. </p> <p class="calibre1">• Case # 2: Witness Protection Program</p> <p class="calibre1">The officials in the Witness Protection Program have lost one of their protected members. You have been asked to determine if</p> <p class="calibre1">1</p> <p class="calibre1">1 − cot (x)</p> <p class="calibre1">is using the identity</p> <p class="calibre1">sin (x)</p> <p class="calibre1">sin (x) − cos (x)</p> <p class="calibre1">If you can prove the identity is true, you will be able to help them find their witness. </p> <p class="calibre1">• Case # 3: Identity Theft</p> <p class="calibre1">We have a case of identity theft! 2 cos (x) has had her identity stolen. Various charges have been made against</p> <p class="calibre1">cot (x) [cos (x) tan (x) + sin (x)]</p> <p class="calibre1">on her behalf. Determine if they are actually the same so that her identity may be returned. </p> <p class="calibre1">• Case # 4: The Stolen Diamond</p> <p class="calibre1">Trig Jewelers is asking for your help. They think that one of their largest diamonds has been stolen and replaced with a diamond that has a fake serial number. The diamond’s serial number is:</p> <p class="calibre1">csc4 (x) − cot4 (x) . </p> <p class="calibre1">The diamond that is now in the case has the following serial number: 2 csc2 (x) − 1. </p> <p class="calibre1">In order to prove that the diamond in the case is an imposter, you need to verify that the two diamonds are actually the same. </p> <p class="calibre1">• Case # 5: Bank Robbers</p> <p class="calibre1">The local police department has apprehended a group of bank robbers. When they ran their names through the criminal database, the database indicated that the bank robbers are on the list of America’s Most Wanted and they are each using an alias. To obtain the rewards for each bank robber, the police department needs to match the criminal with the appropriate alias. They need your help to determine which identity is the appropriate alias. </p> <p class="calibre1">Robbers</p> <p class="calibre1">Aliases</p> <p class="calibre1">cos2 x</p> <p class="calibre1">1. </p> <p class="calibre1">csc x − sin x</p> <p class="calibre1">a. </p> <p class="calibre1">− (sinx + 1)2</p> <p class="calibre1">sin x</p> <p class="calibre1">2. </p> <p class="calibre1">b. </p> <p class="calibre1">sec x</p> <p class="calibre1">sin x + cos x</p> <p class="calibre1">3. </p> <p class="calibre1">2 sin 4x cos 4x</p> <p class="calibre1">c. </p> <p class="calibre1">cos x cot x</p> <p class="calibre1">x</p> <p class="calibre1">4. </p> <p class="calibre1">1 + tan x tan</p> <p class="calibre1">d. </p> <p class="calibre1">sin 8x</p> <p class="calibre1">2</p> <p class="calibre1">sin x − 1</p> <p class="calibre1">tan x</p> <p class="calibre1">5. </p> <p class="calibre1">e. </p> <p class="calibre1">sin x + 1</p> <p class="calibre1">1 + tan x</p> <p class="calibre1"></p> </body> </html> ">
