March 11, 2018

Inverse of y=sin x

6.8 Inverse trig functionsm restrict Domain [ E

,ED

\ x.fi#\ ¥ ' - r

a p

sift'

'

" *III't,

.

..÷.

"

D :[ t,

I ]↳ REEEI

For every × on £1 ,I ] there is a

Y= Siri 'x on [ The,

#2] whose sineis X

March 11, 2018

Domain and range of arcsinYasin

'

'x= arcsinx

Ex.

.

sin. ' G) = # a

sin. ' (E) =f

sin. '(

. E)=I

.

O4

q§

% ¥5tIy.sinixiso@fC.x)= - flx ) Sir 'f×)= - sinkx )

March 11, 2018

Examples

March 11, 2018

Arc cosine

Y = Cost ×

Forevery × in El , if there is a

Y= Cost'

x value on the interval [0,1T ]whose cosine is × .

March 11, 2018

Domain and range of arc cosine

IEx z✓ → •

Cos "( ¥2 ) =3I→ .

4

cos'

'

( FE ) =I .

6

- .@

cos. ' ftz) = It3

March 11, 2018

Examples

March 11, 2018

Identities with arccos and arcsin

t.at O_O*-

sin'

'Cx)tco5' ( × )Cost 'X + cos

'fx)=T2-. .

March 11, 2018

arc tangent

sin' 'fB )

:#¥!y=+anx• f-

a

tariff'Is!oaa0

:an

'

'tx)= - fan"%@ tariffs)tail ( 1 )#3 4

March 11, 2018

Examples

March 11, 2018

arc cosecant

arc secant

arc cotangent

iqiitne=¥¥=csax→' Fcscx

# oD:EE

, 'E ]= y=sei' × →

y=seTTDfo,

it ]=y=coHx → y= fan

P:@

,it ]

March 11, 2018

Graphs

t

March 11, 2018

Defined to satisfy:

←

[ IT, #k] or [ it

, 3H2]-

.

March 11, 2018

Note:

March 11, 2018

Example:

(Draw a triangle)

Es EE.2F 3¥ in JE- - . - .

opts- hyp

#yFz2 = VF

March 11, 2018

:To EE,

ITcot ( cos

' fez) t.int 't 's))cot ( 5¥ + ( ' 'E)) = cot 4¥ = cot 25

=

EE . to . E

March 11, 2018

March 11, 2018

sohe

# E -

C @a2tb2=c2

f i 1/2+32 = c2

�3�C = ytxfq

see (a) =hayf÷, =

' t¥*

March 11, 2018

6 ,•

St. Louis

179¥&D↳b6}•

180T

Plane

Chicago

P.

407 5-every 5th