sem 2 precalc

Degrees → Radians

multiply by π/180

Radians → Degrees

multiply by 180/π

Arc Length

s = rθ

Sector Area (radians)

A = ½r²θ

Sector Area (degrees)

A = (θ/360)πr²

Pythagorean Theorem

a² + b² = c²

Sine

sinθ = opposite/hypotenuse

Cosine

cosθ = adjacent/hypotenuse

Tangent

tanθ = opposite/adjacent

Cosecant

cscθ = 1/sinθ

Secant

secθ = 1/cosθ

Cotangent

cotθ = 1/tanθ

Law of Sines

sinA/a = sinB/b = sinC/c

Law of Cosines

c² = a² + b² − 2abcosC

Law of Cosines for Angle

cosC = (a² + b² − c²)/(2ab)

Triangle Area with Trig

A = ½ab sinC

Exponential Growth

base > 1

Exponential Decay

0 < base < 1

Exponential Form

y = abˣ

exponential equation rules

Same Base Multiplication Rule a^m · a^n = a^(m+n)

Same Base Division Rule a^m / a^n = a^(m−n)

Power to a Power Rule (a^m)^n = a^(mn)

Negative Exponent Rule a^(−n) = 1/a^n

Fractional Exponent Rule a^(1/n) = nth root of a

General Fractional Exponent Rule a^(m/n) = nth root of (a^m)

Logarithmic Form

log_b(x) = y means bʸ = x

Product Rule

log_b(MN) = log_b(M) + log_b(M)

Quotient Rule

log_b(M/N) = log_b(M) − log_b(N)

Power Rule

log_b(Mᵖ) = p log_b(M)

Natural Log

ln(x) = log base e

Exponential Asymptote

y = 0

Logarithmic Asymptote

x = 0

Reference Angle QI

θ

Reference Angle QII

180° − θ or π − θ

Reference Angle QIII

θ − 180° or θ − π

Reference Angle QIV

360° − θ or 2π − θ

Coterminal Angles Degrees

θ ± 360°

Coterminal Angles Radians

θ ± 2π

45-45-90 Triangle Ratio

1 : 1 : √2

45-45-90 Pattern

x, x, x√2

30-60-90 Triangle Ratio

1 : √3 : 2

30-60-90 Pattern

x, x√3, 2x

0° in radians

0

30° in radians

π/6

45° in radians

π/4

60° in radians

π/3

90° in radians

π/2

180° in radians

π

270° in radians

3π/2

360° in radians

2π

sin(0°)

0

cos(0°)

1

tan(0°)

0

sin(30°)

1/2

cos(30°)

√3/2

tan(30°)

√3/3

sin(45°)

√2/2

cos(45°)

√2/2

tan(45°)

1

sin(60°)

√3/2

cos(60°)

1/2

tan(60°)

√3

sin(90°)

1

cos(90°)

0

tan(90°)

undefined

ASTC Quadrant I

all positive

ASTC Quadrant II

sin and csc positive

ASTC Quadrant III

tan and cot positive

ASTC Quadrant IV

cos and sec positive