Calculus Maximus – Appendix A Vocabulary

37 vocabulary flashcards summarizing essential trigonometric identities, linear-equation forms, function properties, exponent and logarithm rules, and key geometric area/volume formulas from the Precalculus review in Calculus Maximus Appendix A.

Reciprocal Identity for Secant

sec x = 1 ⁄ cos x

Reciprocal Identity for Cosecant

csc x = 1 ⁄ sin x

Reciprocal Identity for Cotangent

cot x = 1 ⁄ tan x

Quotient Identity for Tangent

tan x = sin x ⁄ cos x

Quotient Identity for Cotangent

cot x = cos x ⁄ sin x

Pythagorean Identity (Sine–Cosine)

sin² x + cos² x = 1

Pythagorean Identity (Tangent–Secant)

1 + tan² x = sec² x

Pythagorean Identity (Cotangent–Cosecant)

1 + cot² x = csc² x

Double-Angle Identity for Sine

sin 2x = 2 sin x cos x

Double-Angle Identity for Cosine (General)

cos 2x = cos² x – sin² x

Double-Angle Identity for Cosine (Cos Only)

cos 2x = 2 cos² x – 1

Double-Angle Identity for Cosine (Sin Only)

cos 2x = 1 – 2 sin² x

Slope-Intercept Form

y = mx + b, where m is slope and b is y-intercept

Point-Slope Form

y – y₁ = m(x – x₁)

Normal Line

A line perpendicular to the tangent line at a given point

Radical Rule

If x² = a, then x = ±√a

Even Function

f(–x) = f(x) for all x in the domain

Odd Function

f(–x) = –f(x) for all x in the domain

Zero Exponent Rule

a⁰ = 1, provided a ≠ 0

Product Rule for Exponents

aᵐ · aⁿ = aᵐ⁺ⁿ

Quotient Rule for Exponents

aᵐ ⁄ aⁿ = aᵐ⁻ⁿ

Negative Exponent Rule

a⁻ᵐ = 1 ⁄ aᵐ, a ≠ 0

Power-of-a-Power Rule

(aᵐ)ⁿ = aᵐⁿ

Natural Log of 1

ln 1 = 0

Natural Log of e

ln e = 1

Log Product Rule

ln (mn) = ln m + ln n

Log Quotient Rule

ln (m ⁄ n) = ln m – ln n

Log Power Rule

ln (mⁿ) = n ln m

Change-of-Base Formula

log_b y = x ⇔ y = bˣ

Area of a Triangle

A = ½ bh

Area of an Equilateral Triangle

A = (√3 ⁄ 4) s²

Area of a Circle

A = πr²

Circumference of a Circle

C = 2πr

Volume of a Sphere

V = (4⁄3)πr³

Surface Area of a Sphere

SA = 4πr²

Volume of a Cylinder

V = πr²h

Volume of a Cone

V = (1⁄3)πr²h