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## 6.2.2 Notes

by: Katelynn Jones

65

0

22

# 6.2.2 Notes MATH 113

Katelynn Jones
UA
GPA 3.4
- Precalculus Trigonometry
Phylisicia carter

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## About this Document

COURSE
- Precalculus Trigonometry
PROF.
Phylisicia carter
TYPE
Class Notes
PAGES
22
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 22 page Class Notes was uploaded by Katelynn Jones on Tuesday September 29, 2015. The Class Notes belongs to MATH 113 at University of Alabama - Tuscaloosa taught by Phylisicia carter in Fall 2015. Since its upload, it has received 65 views. For similar materials see - Precalculus Trigonometry in Mathematics (M) at University of Alabama - Tuscaloosa.

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Date Created: 09/29/15
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Em 1 CW thde w twccm mm M m m 7 EM Cw CW CXCCX mam camcwx g cm cmw m quotXi39CCgCWC cw CR O mammal mag m M us 39 Cm O39za o 5 4 La qmr 619 m 68M 60 UGO n 00 w ambibww g F wa mg ms 0qu c c 0mm Lawn m 003 CM rm 1 ms Gamma Cqmms mm K33 mama furA mcmm CXCC mm Q Cm Mt SS O w COM 0640 pmem xpcmu wig mm e CXCN MES m UKRQUMC 8mm SUM J 39 t z cL I 39 3 My V 1 FitL 3 A Paint t To verify an identity start with the more complicated side and transform it in a stepbystep fashion until it is identical to the other side It is sometimes helpful to verify an identity by rewriting One of the sides in terms of Sines and cosines and then simplifying the result Example Verify the identity tan x cos x 2 sin x sec 9 cos 6 tan 9 sin 9 secx a cscx t anx 1 secx cscx tanx 1 tan x tan y sin x cos y cos x sin y 1 ta x tan 3 E cosx cos y sin x sin 31 J 135 m 535 2 quot 1 V 1 g I I EM quot3quotquot Sim 39 39e 5m Ej amg 3 51121 2 mg 3 w i ms 391 52m 391 iiii355 ii ga 2 3 ms 5 mg i Sm 3 ag a 3m 33 s a gm 39ng mg i d F r 5 056 9 7311162 7 C059 55in92 74 DJ sin2 t C052 t 2 5111 t 1 wt2 1 Example Complete the identity cscx sinx cos x sinx cos x2 1251nxc03x Example Rewrite the fellowing expression in terms of the given function tanx CGtx secx cscx tanx SECX 1 secx tan u CSC x tam2 x csc x COS x and sin 3 SEETIUN 6 SM M53 DIFFERENCE FGRMHMS PART 1 Sum and Difference Formulas for Cosines and Sines Example cos60 45 In M4 r k l s L39 f i 3 S V a lquot 1 397 3 IL I39 quot 45 KT quot quot Example COS if 71x 6 LL39s i a w 13 L gi ci 433 w uh 54 mm 5 511qu 53 am will H Um EL 39i Jk jxfn 39 Li M 5 13 VJ La 39 113 7 397quot g V J r irh 39 li lv r r23 Kuhn1 i39 m 39 r39 Ema srtgmw ramzasig M La g i f s Sam3935 u l 2 mm i3 aw W3 In am i 5124 139 35M 4L3 MATH 1133 SECTION 62 SM AND DIFFERENCE FORP1ULASPART 1 Ni I H 113 t 2 lt lt3 d 13 lt lt2 fangs 31 a 2mm cos 22 B Jr 4 1 Li L h at W mm Example Find the exact value of the expressions C0301 B Si CCI and tana B under the following conditions 12 8 lies in Quadrant I I 15 sin x a lies in Quadrant I and Sin 13 j QT if if l U 57 Example Write the expression as the sine cosine or tangent of an angle Then nd the exact value of the expression 3111550603350 C0555 Si 350 n 1139 11 1r sm cos cos sm 2 6 2 6 Example Verify the identity sin 6 cos 6 nquot ertrquot JV 1 7 quot1quot i r39nrr st 7 quotquot quot13993quot39r 392 7 i ELLTSLlE 5331 he it i39 may PURE Lyon 5 i quotof i i Example In the following problem the expression is the right side of the formula for cosa B With particular values for a and 3 Write the expression as the cosine of an angle Find the exact value of the expression cos65 cos20 sin65 sin20 lt1 3quotgt lt1 39 3 C03 12 COS 5m 51114 Example Use one or more of the six sum and difference identities to nd the exact value of the expression sin180 30 Sin225 fit an 52 53 AND Bljiwm imjg Sum and Difference Formulas fol Tangent 43973 ya 5 7 2 m I M w 339 quotw m 39 39 9 m gt LL 3 39 v P Ami2 52 quot4 n l a 311 355mm was ilk3 iimf Wm 5 N mi quotan engsiem 5132 E11111 3155gg ssnyi n4 vat43221 231191 ajE tTh ELTLE 133 quot a libg1 397 3943 139 1 391 3 E quotL a 391 2i 11 M la Emil I L111 i 0 000 U 00 450 5600 Colt1 Nle d 2 90quot g 120 4 51 6 tan 6 O wla Unde ned 150 Fl 3 Sn II it 2 180 ml Hm w EE 270O 0 3 2 3000 J CD 0 225 111 330 27 2 360 tanQ 0 Unde ned Wm J3 Example Decide Whether the following statement is true or false tan 75 tan 30 tan 45 Marlow 22 mo DEEfriammn E omwmo ii Pam 25 MME H HE Example Find the exact value of the following expression Rationalize the denominator t 11111r m 6 4 an H tan 105 Example Write the expression as the sine cosine or tangent of an angle Then find the exaet value of the expression tan 5 tan 55 7 1 tan 5 tan 550 7 15 xi 39 M 5 1 T er m it 93 z ES M a 1 i i 12 1e w P if ii ii i if P e 2 Example Find the exact value by using a difference identity t 1139 an K r Example Find the exact value of tan a 3 under the given conditions ltBltn t7 5 ltlt31r 8n mar 81 a 2cos 172 liafxmx 692 some Ee m EPli39 2 Example Rewrite the expression as a simpll ed expression containing one term 6030 3COS a sincr 33131 a 2 Example Complete the identity tan 139 9 z

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