Trig identities Flashcards
Sin(α + β) =
Sin(α)Cos(β) + Cos(α)Sin(β)
Sin(α - β) =
Sin(α)Cos(β) - Cos(α)Sin(β)
Cos(α + β) =
Cos(α)Cos(β) - Sin(α)Sin(β)
Cos(α - β) =
Cos(α)Cos(β) + Sin(α)Sin(β)
Tan(α + β) =
Tan(α) + Tan(β)/ 1 - Tan(α)Tan(β)
Tan(α - β) =
Tan(α) - Tan(β)/ 1 + Tan(α)Tan(β)
Sin(2α) =
2Sin(α)Cos(α)
Cos(2α) =
Cos^2(α) - Sin^2(α)
2Cos^2(a) -1
1- 2sin^2(a)
Tan(2α) =
2Tan(α)/1 - Tan^2(α)
Cos^2(α) =
1/2 + Cos(2α)/2
Sin^2(α) =
1/2 - Cos(2a)/2
Sin(α)/Cos(α) =
Tan(α)
Cos(α)/Sin(α) =
Cot(α)
Cos(-α) =
Cos(α)
Sec(-α) =
Sec(α)
Sin(-α) =
-Sin(α)
Csc(-α)
-Csc(α)
Tan(-α) =
-Tan(α)
Cot(-α) =
-Cot(α)
Sin^2(α) + Cos^2(α) =
1
Sec^2(α) - Tan^2(α) =
1
Csc^2(α) - Cot^2(α) =
1
sinh(x) =
(e^x - e^-x) / 2
cosh(x) =
(e^x + e^-x) / 2
tanh(x) =
sinh(x) / cosh(x)
or
(e^x - e^-x) / (e^x + e^-x)
csch(x) =
1 / sinh(x)
or
2 / (e^x - e^-x)
sech(x) =
1 / cosh(x)
or
2 / (e^x + e^-x)
coth(x) =
1 / tanh(x)
or
(e^x + e^-x) / (e^x - e^-x)
cosh^2(x) -sinh^2(x) =
1
sinh(2x) =
2cosh(x)sinh(x)
or
(e^2x - e^-2x) / 2
cosh(2x) =
cosh^2(x) + sinhh^2(x)
or
(e^2x + e^-2x) / 2
cosh^2(x) =
(cosh(2x) + 1) / 2
cosh(-x) =
cosh(x)
sinh(-x) =
-sinh(x)
tanh^2(x) + sech^2(x) =
1
coth^2(x) - csch^2(x) =
1
