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