Trig / Hyperbolic Functions / Physical App Equations Flashcards
tan(θ) =
sinθ/cosθ
cot(θ) =
cos(θ)/sin(θ)
? + cos²(θ) = 1
sin²(θ)
sec²(θ) - ? = 1
tan²(θ)
csc²(θ) - ? = 1
cot²(θ)
1/sin(θ) =
csc(θ)
1/cos(θ) =
sec(θ)
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)
sin(2*θ) =
2sin(θ)cos(θ)
cos(2*θ) =
All the same:
cos²(θ)-sin²(θ) OR
2cos²(θ) - 1 OR
1 - 2sin²(θ)
cos²(θ) =
(1+cos(2*θ))/2
sin²(θ) =
(1-cos(2*θ))/2
tan²(θ) =
(1-cos(2θ))/(1+cos(2θ))
cos(0) =
1
cos(180) =
-1
cos(90) AND cos(-90) =
0
sin(0) OR sin(180) =
0
sin(90) =
1
sin(270) =
-1
derive: sin(x)
cos(x)
derive: cos(x)
-sin(x)
derive: tan(x)
sec²(x)
derive: sec(x)
sec(x) * tan(x)
derive: csc(x)
-csc(x) * cot(x)
derive: cot(x)
-csc²(x)
derive: sin^-1(x)
1 / √(1-x²)
derive: cos^-1(x)
-1 / √(1-x²)
derive: tan^-1(x)
1 / (1+x²)
integrate: cos(x)
sin(x)
integrate: sin(x)
-cos(x)
integrate: sec²(x)
tan(x)
integrate: sec(x)*tan(x)
sec(x)
integrate: csc(x) * cot(x)
-csc(x)
integrate: csc²(x)
-cot(x)
integrate: tan(x)
ln( [abs value of] sec(x) )
integrate: sec(x)
ln( [abs value of] sec(x) + tan(x))
tan(0) AND tan(180) =
0
sinh(x) =
(e^x - e^(-x))/2
cosh(x) =
(e^x + e^(-x))/2
sech(x) =
1/cosh(x) OR
2/(e^x + e^(-x))
csch(x) =
1/sinh(x) OR
2/(e^x - e^(-x))
tanh(x) =
sinh(x) / cosh(x) OR
(e^x - e^(-x)) / (e^x + e^(-x))
coth(x) =
1/tanh(x) OR
cosh(x)/sinh(x) OR
(e^x+e^(-x)) / (e^x - e^(-x))
cosh²(x) - ? = 1
sinh²(x)
tanh² + ? = 1
sech²(x)
coth²(x) - ? = 1
csch²(x)
sinh(x + y) =
sinh(x)cosh(y) + cosh(x)sinh(y)
sinh(x - y) =
sinh(x)cosh(y) - cosh(x)sinh(y)
cosh(x + y)
cosh(x)cosh(y) + sinh(x)sinh(y)
cosh(x - y)
cosh(x)cosh(y) - sinh(x)sinh(y)
sinh²(x) =
(-1 + cosh(2*x))/2
sinh(2*x) =
2sinh(x)cosh(x)
cosh²(x) =
(1 + cosh(2*x))/2
cosh(2*x) =
cosh²(x) + sinh²(x)
sinh(0) =
0
cosh(0) =
1
tanh(0) =
0
tanh(2x) =
2*tanh(x) / (1+tanh²(x))
coth(x) - tanh(x) =
2csch(2x)
coth(x) + tanh(x) =
2coth(2x)
derive: sinh(x)
cosh(x)
derive: cosh(x)
sinh(x)
derive: tanh(x)
sech²(x)
derive: coth(x)
-csch²(x)
derive: sech(x)
-sech(x) * tanh(x)
derive: csch(x)
-csch(x) * coth(x)
integrate: cosh(x)
sinh(x)
integrate: sinh(x)
cosh(x)
integrate: sech²(x)
tanh(x)
integrate: csch²(x)
-coth(x)
integrate: sech(x) * tanh(x)
-sech(x)
integrate: csch(x) * coth(x)
-csch(x)
integrate: tanh(x)
ln(cosh(x))
integrate: coth(x)
ln([abs value of] sinh(x))
integrate: sech(x)
tan^-1 (sinh(x))
integrate: csch(x)
ln([abs value of] tanh(x/2))
ln(1) =
0
integrate: ln(b*x)
xln(bx) - x
Force = ?
mass * acceleration
Work =
The Integral of FORCE
Force [Springs] =
k*x
Volume =
area * thickness
mass =
Volume * Density OR
Weight/Gravity
