Trigonometric Derivatives

Recall arccength x in radians

a1K Sink

Costax

f x Sinha cos x fan x x is alirays in radians

Q since

Sin Lx h Sin xd

sin x Limhh o

Trig Identity Cim sinc cosch c 5inch cos Csc Sin exu o

h

5inch l c s nLima

c s x Sin xah o

Limit Laws1 c s h

Lion Singh cos x sin x Limau o u o

Siu h l Css hOy Cim

aLim 2h o u o h

Let o h CIz

length tanca

length h

ang a cain

O 1cos h

sin h e h E tanch

il E stitch E tard5inch Cosch

Lim cosch I Lion 1

h 30 a o c sea T I

squeeze Theorem

im4 5inch 5inchI Lim

aI Cim Ifu Ot 5inch u o u

Observation

can l cosch C cos h it coschLiaro h U 70 h l t cosch

I cos h sinkhLim Limh 70 h It scull h 70 h It al

Ligo sina.ITa

cosch

5inch oCim aliso h12 o

U o zLim It scath 70

Lim l coschO

u 50 h

Conclusion sincx cos Cxda

Same Method cos x Siu x

Good Exercise5in xOther Trigonometric Functions tan xcost c s

Sec x Csc x cotcx 1

T µ tangy sincesecant x cosecant x cotangent x

Quotient Rule

d Cos2Gc sin Ge

a tan Gel Sed LxC S2 x

d Sin x

dSec Cx tan Gc Secca

Crisco

dd

Csc Gc cosGcCst Gc Csc Gc

sink c

Cst Gc sink c cask c iCST x

sink Csc Sink c

Zemark Don't waste your time memorizing these Just

Focus on dz siacal Casca and the definitions

Example y dd taulx

tank Sec2Lx

dd tanto Ida secco see Ga exec x secco

c see cxkdzdsecc.ae

tomb Sec a see Gc c Seccx fan Cso sects

Z Siu CK2 tan a Sec Gccos 3 x

44 d

g Gin Cx

dje Ein Cx cos Gc

Repeats i blocks at tow

d3since cos ex

dsinews sin Cxdx4

Td sinews cos Cxdnt