Summary Engineering Mathematics 1a Formula Sheet

Engineering Maths 1a Formula Sheet

Laws of Logarithms:

logb (x)
loga (x) = a log x (b) = log(b a ) logx (ab) = logx (a) + logx (b)
logb (a)

a
e x ln a = a x logx = logx (a) - logx (b)
b

Trigonometric Identities:

sin(A ± B) ≡ sin A cos B ± sin B cos A cos(A ± B) ≡ cos A cos B ∓ sin B sin A

tan A ± tan B
tan(A ± B) ≡
1 ∓ tan A tan B

cos 2A ≡ cos 2 A - sin 2 A cos 2A ≡ 1 - 2 sin 2 A cos 2A ≡ 2 cos 2 A - 1

cos 2 x + sin 2 x = 1 1 + tan 2 x = sec 2 x cot 2 x - 1 = csc 2 x

Hyperbolic Functions:


e x - e -x e x + e -x e 2x - 1
sinh x ≡ cosh x ≡ tanh x ≡
2 2 e 2x + 1


arcsinh x ≡ ln x + x2 + 1 arccosh x ≡ ln x + x2 - 1 (x ⩾ 1)

1 1+x
arctanh x ≡ ln (|x| < 1)
2 1-x

Hyperbolic Identities:

sinh(A ± B) ≡ sinh A cosh B ± sinh B cosh A cosh(A ± B) ≡ cosh A cosh B ± sinh B sinh A

tanh A ± tanh B
tanh((A ± B) ≡
tanh
1 ± tanh A tanh B

cosh 2x ≡ cosh 2 x + sinh 2 x cosh 2x ≡ 2 cosh 2 x - 1 cosh 2x ≡ 2 sinh 2 x + 1

cosh 2 x - sinh 2 x = 1 1 - tanh 2 x = sech 2 x coth 2 x - 1 = csch 2 x