learn · audeac — Interactive IB Mathematics

SOH–CAH–TOA

Ch 1

\sin\theta = \tfrac{\text{opp}}{\text{hyp}},\;\; \cos\theta = \tfrac{\text{adj}}{\text{hyp}},\;\; \tan\theta = \tfrac{\text{opp}}{\text{adj}}

Pythagoras

Ch 1

a^2 + b^2 = c^2

Sine rule

Ch 1

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Cosine rule

Ch 1

c^2 = a^2 + b^2 - 2ab\cos C

Triangle area

Ch 1

\text{Area} = \tfrac{1}{2}ab\sin C

SOH-CAH-TOA

Ch 1

\sin=\tfrac{o}{h},\cos=\tfrac{a}{h},\tan=\tfrac{o}{a}

Sine / cosine rule

Ch 1

\tfrac{a}{\sin A}=\tfrac{b}{\sin B},\;\; a^2=b^2+c^2-2bc\cos A

Area & arc/sector

Ch 1

\text{Area}=\tfrac12 ab\sin C,\;\; s=r\theta,\; A=\tfrac12 r^2\theta

Common trap

Ch 1

Arc/sector formulas need θ in RADIANS; sine rule has an ambiguous (two-angle) case.

Pythagorean identity

Ch 2

\sin^2\theta + \cos^2\theta = 1

Ratio identity

Ch 2

\tan\theta = \frac{\sin\theta}{\cos\theta}

Double angle

Ch 2

\sin 2\theta = 2\sin\theta\cos\theta,\quad \cos 2\theta = \cos^2\theta - \sin^2\theta

General sinusoid

Ch 2

y = a\sin(b(x+c)) + d

amplitude

|a|

, period

360°/b

, shift

c

, midline

d

.

Period of tan

Ch 2

\tan x

repeats every

180°

(others every

360°

).

Solving sin x = k

Ch 2

Solutions

x

and

180° - x

, plus

360°

multiples.

Solving cos x = k

Ch 2

Solutions

x

and

360° - x

(i.e.

\pm x

).

Solving tan x = k

Ch 2

One solution then add

180°

repeatedly.

Pythagorean

Ch 2

\sin^2\theta + \cos^2\theta = 1

Double angle

Ch 2

\sin2\theta = 2\sin\theta\cos\theta,\;\cos2\theta = 1-2\sin^2\theta

y = a sin(b(x−c))+d

Ch 2

amp |a|, period 2π/b, horizontal shift c, vertical shift d.

Common trap

Ch 2

Solving trig equations: give ALL solutions in the stated interval (use the period).