Precalculus Flashcards

functions general form

f(x) = ax² + bx² + c

functions standard form

f(x) = a(x-h)² + k

Axis of symmetry

k = f(h), f(-b/2a)

Power function

f(x) = kx^p

Direct variation

y = kxⁿ, k = y/xⁿ

Inverse variation

y= k/xⁿ, k = xⁿy

Joint variation

• if x varies directly with both y and z, x = kyz

• if x varies directly with y and inversely with z, x = ky/z

Period

2π/frequency

Frequency

2π/period

Amplitude

(Maximum - Minimum) / 2

Midline formula

(Maximum + Minimum) / 2

Standard trig function form

y = D + A(function) [B(x - C)]

Pythagorean theories

• sin²ø + cos²ø = 1

• tan²ø + 1 = sec²ø

• 1 + cot²ø = csc²ø

sinA + sinB

2sin[A+B)/2] cos[A-B)/2]

sinA - sinB

2sin[A-B)/2] cos[A+B)/2]

cosA - cosB

-2sin[A+B)/2] sin[A-B)/2]

cosA + cosB

2cos[A+B)/2]cos[A-B)/2]

Law of sines

sinA/a = sinB/b = sinC/c

Law of cosines

• a² = b² + c² - 2bc(cosA)

• b² = a² + c² - 2ac(cosB)

• c² = a² + b² - 2ab(cosC)

sin(A + B)

sinAcosB + sinBcosA

sin(A - B)

sinAcosB - sinBcosA

cos(A+B)

cosAcosB - sinAsinB

cos(A - B)

cosAcosB + sinAsinB

tan(A+B)

• (tanA + tanB) / (1 - tanAtanB)

• (sinAcosB + sinBcosA) / (cosAcosB - sinAsinB)

tan(A - B)

• (tanA - tanB) / (1 + tanAtanB)

• (sinAcosB - sinBcosA) / (cosAcosB + sinAsinB)

cos2ø

• cos2ø = cos²ø - sin²ø

• cos2ø = 2cos²ø - 1

• cos2ø = 1 - 2sin²ø

sin2ø

2sinøcosø

X value, converting polar to rectangular

x = rcosø

Y value, converting polar to rectangular

y= rsinø

Equations converting rectangular to polar

• r² = x² + y²

• ø = tan^-1(y/x)

Roses formulas

• r = asin(nø)

• r = acos(nø)

Cardioid Formula

• r = a + bsinø

• r = a + bcosø

• b = a

Limaçon Formulas

• r = a + bsinø

• r = a + bcosø

Lemniscate sin formulas

• r² = a²sin(2ø)

  • r = a√sin(2ø)

  • r = a√-sin(2ø)

Lemniscate cos formulas

• r² = a²cos(2ø)

  • r = a√cos(2ø)

  • r = a√-cos(2ø)

Horizontal distance

x(t) = (v₀cosØ)t

Vertical height

y(t) = h₀ + (v₀sinØ)t - 1/2gt²