PC 12 Skill 19a: I can simplify and prove trigonometric identities, using the reciprocal, quotient, Pythagorean, sum/difference, and double-angle identities (6.1) Reciprocal & Quotient Identities csc x = sec x = cot x = tan x = cot x = Task 1: Simplify and state non-permissible values. a) !"# $ #%& $ #%& $ !"# $ b) ’(& $ ) #*! $ !#! $ + c) !"’ $ !#! $ !"# $ Task 2: More fraction fun! a) ,-#%& $ !"# $ !"# $ b) ./0 1 $-#%& $ #%& $ !"# $ c) ’(& $-#%& $ #*! $ !#! $ ’(& $ I 1 I sink cosx tank recidenlines Sinx Cosa cosC sink cotxtanx.to xx tame sina.io xx cotx cosmo tan I cost ask cofe tank sink sink cotx.co x cosse cot2x size cots nonperm cook 40 cost si x ttzs ztn.no ICOFK tg.sn ogysecxtsinx sina.CH cost l t sink cosx I t ts cotx Seck oscxtanx sinx sink Non permit 2 sink singe 40 Cost to K 0 12in KF It2Tn
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PC 12 Skill 19a: I can simplify and prove trigonometric identities, using the reciprocal, quotient, Pythagorean, sum/difference, and double-angle identities (6.1)
Reciprocal & Quotient Identities
csc x = sec x = cot x =
tan x = cot x = Task 1: Simplify and state non-permissible values.
a) !"# $#%& $#%& $!"# $
b) '(& $)#*! $!#! $+
c) !"' $!#! $ !"# $
Task 2: More fraction fun!
a) ,-#%& $ !"# $!"# $ b) ./0
1$-#%& $#%& $ !"# $
c) '(& $-#%& $ #*! $!#! $ '(& $
I 1 Isink cosx tank
recidenlinesSinx CosacosC sink
cotxtanx.toxxtame sina.ioxx
cotx cosmotan I
cost askcofe tank sink sinkcotx.co x cossecot2x size cots
nonpermcook40
cost sixttzsztn.no ICOFK tg.snogysecxtsinxsina.CH
cost ltsink cosx
It ts cotx Seckoscxtanx
sinx sink Nonpermit2sink singe40 Cost to
K 0 12in KF It2Tn
PC 12 Skill 19a: I can simplify and prove trigonometric identities, using the reciprocal, quotient, Pythagorean, sum/difference, and double-angle identities (6.1)
Task 3: Calculate: 0341 )56+ + ./0
1 )56+
Pythagorean Identities:
./018 + 03418 = , ./:18 + , = .0.18 , + :;418 = 0<.18
Task 3: Prove
1) ./018 + 03418 + :;418 = 0<.18 2) , − ./01$:;41$ = ./01$ Skill 19a Ticket:
1) Simplify and state non-permissible values #*! $'(&$
2) Simpliy 0341$
,>./0$
For any point on the unit circle (x, y), $1 + ?1 = ,, since the radius of the circle = 1 and we know x = cos θ and y = sin θ
EE
444 1
Tino Tino TinoCoto I Csc
sink
dKtankI sink_cos3Csink sink t cos2atan2k
I cos3ctsin3c I cos2x cos3cta.in
Ksin2K sin2K
1 1 2 csc xI cosx l cosx
common denomI 1 cos c I cos c
PC 12 Skill 19a: I can simplify and prove trigonometric identities, using the reciprocal, quotient, Pythagorean, sum/difference, and double-angle identities (6.1)
leg2tleg2_hyp2qxhYP2leg2
1eg2sin2xtcos3cTs9
s II's3y f prove this pythagoreanT identity
SIMPLIFY
II Fix
Csecx
II C Ty2t I
cosh
Y2txZ r2
I cosse
sink
Simplify to one of the three primary TRIG ratios.
NpASK 1AHHH
a Sinitta l cosx sink I cos3c
I cosx C cos'D sink t.E.gs c fsina.cosxsinxitanx tanxcossD 2 E
2 1 uc Et E citxxi x
i t E Foam II Ea I
b cost Sino tocsinNP ssE tanx
y2 202 1
sin WSO Sino F O Te680 0OSO SMO y2tyc2
Z
sink si sO 0 11 I 0
Sino WSO
Csco t Seco
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