Log and trig formulas

Logarithmic form

Logarithmic form

logₐx = y

Exponential form

aᵞ = x

logₐ1 =

0

logₐa =

1

logₐaᵡ =

x

aᶩᵒᶢᵃᵡ

x

x₁ ≠ x₂

logₐx₁ ≠ logₐx₂

logₐx₁ = logₐx₂

x₁ = x₂

lnx =

logₑx

logₐ(uw) =

logₐu + logₐw

logₐ(u/w) =

logₐu - logₐw

logₐ(uᶜ) =

clogₐu where c is a real number

logₐ(u + w) ≠

logₐu + logₐw

logₐ(u - w) ≠

logₐu - logₐw

A line is

180° or 0°

Positive angles go

Counter-clockwise

Negative angles go

Clockwise

The max of the l₁ is

360°

The min of the l₁ is

There is no minimum

Co-terminal angles

Different angle measurements with the same terminal (l₂) and initial (l₁) side

180° =

π radians

1° =

π/radians

1 radian =

(180/π)°

sinθ

a(opp)/c(hyp)

cosθ

b(adj)/c(hyp)

tanθ

a(opp)/b(adj)

secθ

c(hyp)/b(adj) or 1/cosθ

cscθ

c(hyp)/a(opp) or 1/sinθ

cotθ

b(adj)/a(opp) or 1/tanθ

sin²θ + cos²θ =

1

tan²θ + 1 =

sec²θ

1 + cot²θ =

csc²θ