Trigonometry Review Table -...
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© Houghton Mifflin Company, Inc. TRIGONOMETRY Definition of the Six Trigonometric Functions Right triangle definitions, where 0 2. Circular function definitions, where is any angle. tan y x cot x y cos x r sec r x sin y r csc r y θ x y y x r (x, y) r = x 2 + y 2 tan opp adj cot adj opp cos adj hyp sec hyp adj sin opp hyp csc hyp opp Adjacent θ Hypotenuse Opposite x y 240° 90° 0° 360° 330° 30° 150° 210° 315° 45° 135° 225° 300° 60° 120° 270° 180° (0, 1) 1 2 2 ) ( , , − − − − − − − 0 π π 2 6 4 3 3 2 3 3 4 4 4 6 6 6 2 π π π 2π 3π 4π 5π 3π 5π 7π 5π 7π 11π π (0, − 1) (− 1, 0) (1, 0) 3 1 2 2 ) ( , − 3 1 2 2 ) ( , − 3 1 2 2 ) ( , − 3 2 ) ( , − 2 2 2 2 ) ( , − 2 2 2 1 2 2 ) ( 3 , 1 2 2 ) ( 3 1 2 2 ) ( , 3 1 2 2 ) ( , 3 2 ) ( , 2 2 2 2 ) ( , 2 2 2 < < Reciprocal Identities Tangent and Cotangent Identities Pythagorean Identities Cofunction Identities Reduction Formulas Sum and Difference Formulas Double-Angle Formulas Power-Reducing Formulas Sum-to-Product Formulas Product-to-Sum Formulas cos u sin v 1 2 sinu v sinu v sin u cos v 1 2 sinu v sinu v cos u cos v 1 2 cosu v cosu v sin u sin v 1 2 cosu v cosu v cos u cos v 2 sin u v 2 sin u v 2 cos u cos v 2 cos u v 2 cos u v 2 sin u sin v 2 cos u v 2 sin u v 2 sin u sin v 2 sin u v 2 cos u v 2 tan 2 u 1 cos 2u 1 cos 2u cos 2 u 1 cos 2u 2 sin 2 u 1 cos 2u 2 tan 2u 2 tan u 1 tan 2 u cos 2u cos 2 u sin 2 u 2 cos 2 u 1 1 2 sin 2 u sin 2u 2 sin u cos u tanu ± v tan u ± tan v 1 tan u tan v cosu ± v cos u cos v sin u sin v sinu ± v sin u cos v ± cos u sin v secx sec x cotx cot x cscx csc x tanx tan x sinx sin x cosx cos x sec 2 x csc x cot 2 x tan x csc 2 x sec x tan 2 x cot x sin 2 x cos x cos 2 x sin x 1 cot 2 x csc 2 x 1 tan 2 x sec 2 x sin 2 x cos 2 x 1 tan x sin x cos x cot x cos x sin x csc x 1 sin x cos x 1 sec x cot x 1 tan x sin x 1 csc x sec x 1 cos x tan x 1 cot x
Transcript of Trigonometry Review Table -...
© Houghton Mifflin Company, Inc.
TRIGONOMETRY
Definition of the Six Trigonometric FunctionsRight triangle definitions, where 0 2.
Circular function definitions, where is any angle.
tan � �yx cot � �
xy
cos � �xr sec � �
rx
sin � �yr csc � �
ry
θx
y
y
x
r
(x, y)r = x2 + y2
�
tan � �oppadj
cot � �adjopp
cos � �adjhyp
sec � �hypadj
sin � �opphyp
csc � �hypopp
Adjacent
θHypotenuse
Opp
osite
x
y
240°
90°
0°360°
330°
30°150°
210°315°
45°135°
225°300°
60°120°
270°
180°
(0, 1)12 2 )( , ,−
− −
−
−
−
−
0ππ 2
6
433
23 3
4
4 4
6
6 6
2
ππ
π2π
3π4π 5π
3π
5π 7π
5π
7π 11π
π
(0, −1)
(−1, 0) (1, 0)
3
12 2 )( ,− 3
122 )( ,− 3
122 )( ,− 3
2 )( ,− 222
2 )( ,− 222
12 2 )( 3
,12 2 )( 3
122 )( ,3
122 )( ,3
2 )( , 222
2 )( , 222
< � < ��
Reciprocal Identities
Tangent and Cotangent Identities
Pythagorean Identities
Cofunction Identities
Reduction Formulas
Sum and Difference Formulas
Double-Angle Formulas
Power-Reducing Formulas
Sum-to-Product Formulas
Product-to-Sum Formulas
cos u sin v �12
�sin�u � v� � sin�u � v��
sin u cos v �12
�sin�u � v� � sin�u � v��
cos u cos v �12
�cos�u � v� � cos�u � v��
sin u sin v �12
�cos�u � v� � cos�u � v��
cos u � cos v � �2 sin�u � v2 � sin�u � v
2 �cos u � cos v � 2 cos�u � v
2 � cos�u � v2 �
sin u � sin v � 2 cos�u � v2 � sin�u � v
2 �sin u � sin v � 2 sin�u � v
2 � cos�u � v2 �
tan2 u �1 � cos 2u1 � cos 2u
cos2 u �1 � cos 2u
2
sin2 u �1 � cos 2u
2
tan 2u �2 tan u
1 � tan2 u
cos 2u � cos2 u � sin2 u � 2 cos2 u � 1 � 1 � 2 sin2 usin 2u � 2 sin u cos u
tan�u ± v� �tan u ± tan v
1 � tan u tan v
cos�u ± v� � cos u cos v � sin u sin v
sin�u ± v� � sin u cos v ± cos u sin v
sec��x� � sec x cot��x� � �cot x
csc��x� � �csc x tan��x� � �tan x
sin��x� � �sin x cos��x� � cos x
sec��
2� x� � csc x cot��
2� x� � tan x
csc��
2� x� � sec x tan��
2� x� � cot x
sin��
2� x� � cos x cos��
2� x� � sin x
1 � cot2 x � csc2 x1 � tan2 x � sec2 x
sin2 x � cos2 x � 1
tan x �sin xcos x
cot x �cos xsin x
csc x �1
sin x cos x �
1sec x
cot x �1
tan x
sin x �1
csc x sec x �
1cos x
tan x �1
cot x
