Irodov – Problems in General Physics

APPENDICES

1. Basic Trigonometrical Formulas

sine a + cosa a = 1

sect a— tans a =1

cosecs a— cots a =1

sin a •cosec a =1

cos a •sec a= 1

tan a • cot a =1

sin (a ± 13) = sin a cos p ± cos a sin p

cos (a ± fl)---- cos a cos 13 sin a sin 13

tan (a ± ) = 13 tan a ± tan 13

1 tan a• tan 0

—

cot a cot 13 1

cot (c, ± 13) (^) cot 13 ± cot a
sin a—^1 sin a+ sin 13=2 sin at R^ cos a— p
y l+cota a
cos a— ,^1
2 2
sin a sin 13=2 cos a + 13 sin a + 13
Y 1+tan^2 a
sin 2 a= 2 sin a cos a
cos. 2a= cos 2 a— sin 2 a
2 tan a
tan 2a—
2 2
a a^
2 +1^3 — p
cos a + cos 13 = cos^2 cos 2
[3= 2 sin a+P sin —^13
cos a—cos — a 2 2
sin (a ± 13)
1— tang a tan a ±^ tan p =
cot 2a— cote a-1
cos a cos p
sin (a ± p)
2 cot a cot a ± cot 13= ± sin a sin 13
2 sin a sin p= cos (a— 0) — cos (a + 13)
2 cos a cos 13= cos (a— p)H- cos (cc+ p)
2 sin a cos 13= sin (a— p)+ sin (a +13)
,_ cc (^) V 1—cos a
sin — = 2
2
cos a = V 1+cos a
(^2 2)
ea -a — 0
sinh a=
0 a —^ e -a
tanh a =
2
ec`±e—a
ex + 0'
ea +13'
cosh a- 2 cosh a= CO — CL
e —e