The_Cambridge_Handbook_of_Physics_Formulas

32 Mathematics
2.5 Trigonometric and hyperbolic formulas
Trigonometric relationships
sin(A±B)=sinAcosB ±cosAsinB (2.171)
cos(A±B)=cosAcosB ∓sinAsinB (2.172)
tan(A±B)= tanA±tanB
1∓tanAtanB
(2.173)
cosAcosB = 1 [cos(A+B)+cos(A−B)]
2
(2.174)
sinAcosB = 1 [sin(A+B)+sin(A−B)]
2
(2.175)
2
cos 2 A+sin 2 A = 1 (2.177)
1
cosx
sinx
sec 2 A−tan 2 A = 1 (2.178)
0
csc 2 A−cot 2 A = 1 (2.179)
−1
sin2A =2sinAcosA (2.180)
cos2A =cos 2 A−sin 2 A (2.181)
−2
−6
−4
−2
tanx
0
x
2
4
6
tan2A =
2tanA
1−tan 2 A
(2.182)
sin3A =3sinA−4sin 3 A (2.183)
cos3A =4cos 3 A−3cosA (2.184)
sinA+sinB =2sin A+B cos
2 2
sinA−sinB =2cos A+B sin A−B
2 2
cosA+cosB =2cos A+B cos A−B
2 2
cosA−cosB = −2sin A+B sin A−B
2 2
sinAsinB = 1 2 [cos(A−B)−cos(A+B)] (2.176) x
(2.185)
(2.186)
(2.187)
(2.188)
4
2
0
−2
−4
cotx
secx
cscx
cos 2 A = 1 (1+cos2A) (2.189)
2
−6
−4
−2
0
2
4
6
sin 2 A = 1 (1−cos2A) (2.190)
2
cos 3 A = 1 (3cosA+cos3A) (2.191)
4
sin 3 A = 1 (3sinA−sin3A) (2.192)
4