Trigonometry Cheat Sheet Flashcards

Trigonometry formulas and concepts for review.

DMS to Decimal Conversion

Degrees + (Minutes/60) + (Seconds/3600)

SOH-CAH-TOA

Mnemonic for Right Triangle Definitions: Sinθ = Opp/Hyp, Cosθ = Adj/Hyp, Tanθ = Opp/Adj

Cscθ

Hyp/Opp (Reciprocal of Sine)

Secθ

Hyp/Adj (Reciprocal of Cosine)

Cotθ

Adj/Opp (Reciprocal of Tangent)

Pythagorean Identity 1

sin²θ + cos²θ = 1

Pythagorean Identity 2

1 + tan²θ = sec²θ

Pythagorean Identity 3

1 + cot²θ = csc²θ

Mnemonic for Pythagorean Identities

"Silly Cats Try Tricks"

Sin(A±B)

sinAcosB ± cosAsinB

Cos(A±B)

cosAcosB ∓ sinAsinB

Tan(A±B)

(tanA ± tanB)/(1 ∓ tanAtanB)

Mnemonic for Sum & Difference Formulas

"Sine same, cosine change"

Sin(2θ)

2sinθcosθ

Cos(2θ)

cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

Tan(2θ)

2tanθ/(1 - tan²θ)

Sin(θ/2)

±√[(1 - cosθ)/2]

Cos(θ/2)

±√[(1 + cosθ)/2]

Tan(θ/2)

(1 - cosθ)/sinθ = sinθ/(1 + cosθ)

Law of Sines

a/sinA = b/sinB = c/sinC

Law of Cosines

c² = a² + b² - 2abcosC

Triangle Area - SAS

Area = ½absinC

Triangle Area - SSS

Heron's Formula (√[s(s-a)(s-b)(s-c)], s=(a+b+c)/2)

General Solution for sinθ = k

θ = sin⁻¹k + 2πn or π - sin⁻¹k + 2πn

General Solution for cosθ = k

θ = ±cos⁻¹k + 2πn

Polar to Rectangular Conversion

x = rcosθ, y = rsinθ

Rectangular to Polar Conversion

r = √(x² + y²), θ = tan⁻¹(y/x)

Dot Product of Vectors

u·v = u₁v₁ + u₂v₂

Orthogonal Vectors

u·v = 0

Polar Form of Complex Numbers

r(cosθ + isinθ) = rcisθ

Complex Number Multiplication in Polar Form

Multiply magnitudes, add angles