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# Pre-Cal 40S March 12, 2007

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A quick review of last class and more about the Pythagorean Identities. We focused more on the details of presentation and style and whether or not to use equal signs and how to end our proofs.

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### Pre-Cal 40S March 12, 2007

1. 1. A quick review Trigonometric Identities The basic building blocks of all the trigonometric functions are the sine (sin Q and cosine (cos 6’) functions. The Fundamental Identities sin6 121110 = Sing C059 cost) ‘os9 C0t0=C. .. .9_ 1 l s1n0 “*9 7? scc0= “"0 C056
2. 2. sing 6+cos2 6 =1 Which implies -, -, - 2 2 Sm—g C051; 1 sin 9+cos 0_ l '2 + '3 = '1 cos3H cos2H- os36 sin 6 sin 9 sin 0 C -s 1 , l+C0[ 9=CSC 0 [an'6+l= sec2(} I ollaries l+cot26=csc26 sin26+cos38-l tan36+l-sec38 cos20=l—sin30 l= csc26-cot26 tan39=sec3(9_] "“29=1‘C°526 cot36-csc36—l I-sec20—tan2H
3. 3. Let's warm up Simplify each of the following as much as possible: cost sinx + SCC . X‘ C SC I sintpsec gt:
4. 4. Let's warm up Simplify each of the following as much as possible:
5. 5. Let's warm up Simplify each of the following as much as possible: cosx sinx + sccx cscx Co s>< 2m_. x ' ‘I’ I j'iVT)C C-35‘ . "' +- s VW1'1C c0S‘rC I
6. 6. Prove each of the following identities tana(tana+cota) = scc3a cog39_sjn39= 1-2511130 l'“ma _ C°ta"l I+tana cota+I
7. 7. Prove each of the following identities tana(tana + cota) = sec‘ (1 C053 (9 _ 51113 9 = 1- 251113 0 I'amo< (+c: ro< ‘I’ ‘I'svoLI 7-. ‘-004 Ls-a-. u~+_‘__I; D( l—tana _ cota—l l+tana cota+I