Precalculus Formulas

Quadratic Formula

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Radians to Degrees

• 180°/𝜋

Degrees to Radians

• 𝜋/180°

Arc Length

rθ

Area of a Sector

1/2 • r² • θ

Cofunction Identity

sin(x) = cos(𝜋/2 - x)

Percent of Increase/Decrease

Difference/Original = x/100

𝜋/3

(∓ 1/2, ∓ ⎷3/2)

𝜋/6

(∓⎷3/2, ∓1/2)

𝜋/4

(∓⎷2/2, ∓⎷2/2)

Direct Variation

y = kx

Indirect Variation

y = k/x

Exponential Growth/Decay

y = abˣ ; y = a(1+r)ˣ

Pythagorean Identity

sin²x + cos²x = 1

Compound Interest

P(1 + r/n)ⁿᵗ

Exponent Multiplication Rule

aⁿaᵐ= aⁿ⁺ᵐ

Exponent Division Rule

aᵐ/aⁿ

Exponent To a Power Rule

(aⁿ)ᵐ = aⁿᵐ

Midpoint Formula

(\[x₁+x₂\]/2, \[y₁+y₂\]/2)

Equation of a Circle

(x-h)² + (y-k)² = r²

Distance Formula

⎷(x₂-x₁)² + (y₂-y₁)²

Special 45° 45° 90° Triangle

a = s, b = s, c = s⎷2

Special 30° 60° 90° Triangle

long leg = ⎷3･x, short leg = x, hypotenuse = 2x