Trigonometric Functions Speelal Valuda of Trlgonomatrlc FunctlanaAcute angles

Arbitrary angles

Real numbers

1 -

./2 Zr/3\ u 3 2

I "'12 'tz

./3 ^ 2{g5 ' g

0 - 1

0

{33

1

,/3

csc o = hYPopp

sec o = lYPaoJ

cot Q = adjopp

c s c 0 = rb

s e c o = ra

c o t Q = ab

= br

= ar

= ba

i i . . i t l t r l ( :

I t < u < f r2

- ' - 2

O S y 3 n

-t.v. tO . y . n

[.;) "[" + )I z'o)'f r]

opphvpadjhvpoppaai

e e(degrees) (radians) sin 0 cos 0 tan 0 cot 0 sec 0 csc 0s i n 0 =

c o s O =

t a n 0 =

sin 0

cos 0

tan 0

s i n t -

c o s l =

t a n f =

Tri go n ometri c I de ntlti es

0

f i

6

7l

4n5IE

2

lnverse

0 1

1 €2 2^12 .{2TT./3 12 2

1 0

Trlgonometric FunctlonaY c s c t = 1

.,"".',,,i YI

x sec t= +Y c o t l = xx ''.:;''''Y::'

I i r i l i i t r r l ' t

)z = Sin-1 X

)z = COS-1 X

Y = lan-1 x

Y = COI-1 X

/ = Sec-l x

/ = C S C 1 x

- 1 ( x ( 1

- 1 ( x S 1

l " l t t

l " l= t

R

R

Laws of Slnes and Coslnee

csc t= 1/sin f

sec l= 1/cos f

c o t f = l l l a n tsin2 f + cos2 f = 1

1 + tan2 f= SeC2 f

1 + cot2 l= CSC2 f

lsn

tan t = sin t/cos fcot f = cos /sin f

sin (-f) = -sin

cos (-f) = ssgtan (-f) = -tan

t

cos2 u --

= S i n B = S i n C-6- c

SiNAa

a 2 = b 2 + C 2 - 2 b C C O S Ac 2 = a 2 + b 2 - 2 a b c o s Cb2= c2 + a2-2accos B

t Untt Circlesin (u+ v) = sin ucos v+ cos usin vcos (u + v) = cos u cos v- sin u sin v

. t a n u + t a n yt a n ( u + v ) = 1 - t a n u t a n v

sin (u- v) = sin ucos v- cos usin vcos (u - t) - cos ucos v+ sin usin v

. tan u- lanvIan (u-v) - 1 + tan utarw

sin 2u =2 sin u cos uCOS 2U= CoS2 u- Sin2 U1 - 2Sin2 U= 2 COS2 U- 1

2tan uranzu= 1-tefu

' 120'

rss' \ ^\ ( - t ' ; )

60"

tr,6t 7ou"

90"

(o,r)

1so' e'El(-f,.i)

(E'E) , .so"cf l)

(1,0)- 0'

(.f,-i)$:-E) iso'

u l _2 l - l*"#

(*,-f ) \\

31s"

300'

. u 1 - c o s u s i n ulqrr A - ------- - " 2 s i n u 1 + c o s u

1 - c o s 2 uSln4 U= ---

z

sin u cos v = 1/2 [sin (u + v) + sin (u - v)]cos u sin v = 1/2 [sin (u + v) - sin (u - v)]cos u cos v = 1/2 [cos (u + 14 + cos (u - v)]sin u sin v = 112 [cos (u - v) - cos (u + rz)]

1 + c o s 2 u__-z-

i { r i ; r : i } n t : l : 1 " i i ' 1 ,

Eources:Wright, John W. ed. The New York limes Almanac Millennium Edition. Penguin Reference

Table of Trigonometric ldentitieshttp://www.sosmath.com/tri g/l-ri gSltri gS/trig5. htm I

Swokowski, Olnik and Pence. Calculus of a Single Variable, 2nd Edition P.W.S.

f u l i l t l : l i r . { r ' i l t t r r r

$ources:Wright, John W. ed. The New York Times Almanac Millennium Edition. Penguin References

rf,-i r