MTH301 Formulas

A α alpha N ν nu

B β beta Ξ ξ xi

Γ γ gamma O o omicron

∆ δ delta Π π pi

E ϵ, ε epsilon P ρ rho

Z ζ zeta Σ σ sigma

H η eta T τ tau

Θ θ, ϑ theta Υ υ upsilon

I ι iota Φ φ, ϕ phi

K κ kappa X χ chi

Λ λ lambda Ψ ψ psi

M µ mu Ω ω omega

am × an = am+n

(am)n = amn

log(AB) log A + log B

log(A/B) log A − log B

log(An) n log A

logb a logc a

logc b tan A = sin A/ cos A

sec A = 1/ cos A

cosec A = 1/ sin A

cot A = cos A/ sin A = 1/ tan A

sin2 A + cos2 A = 1

sec2 A = 1 + tan2 A

cosec 2A = 1 + cot2 A

sin(A ± B) = sin A cos B ± cos A sin B

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

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

sin 2A = 2 sin A cos A

cos 2A = cos2 A − sin2 A

= 2 cos2 A − 1

= 1 − 2 sin2 A

tan 2A = 2 tan A 1−tan2 A

sin 3A = 3 sin A − 4 sin3 A

cos 3A = 4 cos3 A − 3 cos A

tan 3A = 3 tan A−tan3 A 1−3 tan2 A

sin A + sin B = 2 sin A+B cos A−B sin A − sin B = 2 cos A+B sin A−B

cos A + cos B = 2 cos A+B cos A−B

cos A − cos B = −2 sin A+B sin A−B

2 sin A cos B = sin(A + B) + sin(A − B)

2 cos A sin B = sin(A + B) − sin(A − B)

2 cos A cos B = cos(A + B) + cos(A − B)

−2 sin A sin B = cos(A + B) − cos(A − B)

a sin x + b cos x = R sin(x + φ), where R = a2 + b2 and cos φ = a/R, sin φ = b/R.

If t = tan 1 2 x then sin x = 2t 1+t2 , cos x = 1−t2 1+t2 .

cos x = 1 2 (eix + e−ix) ; sin x = 1 2i (eix − e−ix)

eix = cos x + i sin x ; e−ix = cos x − i sin x