Precalc Chapter 4

just formulas and stuff to remember

Area of Arc

½r²θ

Length of Arc

rθ

Linear Speed

s / t

Angular Speed

θ / t

Damped Trig Function

y = ke^-ctsinwt (starts avg) or y = ke^-ctcoswt (starts most)

Amptitude

a

Period (cos/sin & tan)

cos/sin: 2π/b

tan: π/b

Phase Shift

c/b

Midline

y = d

Frequency

b/2π

D: -1 ≤ x ≤ 1

sin(sin^-1 x) = x

cos(cos^-1 x) = x

D: -∞ < x < ∞

tan(tan^-1 x) = x

D: -π/2 ≤ x ≤ π/2

sin^-1 (sin x) = x

D: 0 ≤ x ≤ π

cos^-1 (cos x) = x

D: -π/2 < x < π/2

tan^-1 (tan x) = x

Law of Sines + what applies to

sinA/a = sinB/b = sinC/c

AAS & ASA

Law of Cosines + what applies to

a² = b² + c² + 2bc cosA

SSA & SAS (order matters)

Area (all)

√s(s-a)(s-b)(s-c)

where s = perimeter/2

Area (SAS)

½bcsinA

SSA Obtuse Rules

1. opp > adj → 1 triangle

2. opp < adj → NO triangle

SSA Acute Rules

1. opp ≥ adj → 1 triangle

2. opp < adj

   1. opp < h → NO triangle

   2. opp = h → 1 triangle

   3. opp > h → 2 triangle

DMS format

degree minute second

_° _’ _”