algebra 2 honors final review

compounded continuously

A = Pe^rt

compounded interest

A = P(1+r/n)^nt

change of base

loga/logb

arithmetic explicit rule

an = a1 + d(n-1)

arithmetic recursive rule

an = an-1 + d

arithmetic sum

Sn = (a1 + an/2)n

geometric explicit rule

an = a1( r) ^n-1

geometric recursive

an = (an-1)r

geometric sum

a1 (1-r^n/1-r)

infinite geometric sum

a1/1-r

area of triangle

1/2bcsinA

height of triangle

bsinA

inverse sin, csc, tan

quadrant 1 and 2

inverse cos, sec, cot

quadrant 1 and 4

A > 90, a>b

one triangle

A > 90, a<b

no triangle

A < 90, a<bsinA

no triangle

A < 90, a = bsinA

one right triangle

A < 90, a>bsinA

two triangles

pythagorean identity

cos²x + sin²x = 1

pythagorean version 1

1 - sin²x = cos²x

pythagorean version 2

1 - cos²x = sin²x

pythagorean version 3

sec²x = tan²x + 1

pythagorean version 4

csc²x = cot²x + 1

sin(x+y)

sinxcosy + cosxsiny

sin(x-y)

sinxcosy - cosxsiny

cos(x+y)

cosxcosy - sinxsiny

cos(x-y)

cosxcosy + sinxsiny

tan(x+y)

tanx + tany/1 - tanxtany

tan(x-y)

tanx - tany/1 + tanxtany

sin2x

2sinxcosx

cos2x version 1

2cos²x -1

cos2x version 2

2sin²x - 1

cos2x version 3

cos²x - sin²x

tan2x

2tanx/1 - tan²x

sinx/2

1-cosx/2 (square root)

cosx/2

1 + cosx/2 (squareroot)

tanx/2

1-cosx/1+cosx (squareroot)

circle equation

(x-h)² + (y-k)² = r²

ellipse equation

(x-h)²/# + (y-k)²/# = 1

hyperbola equation

(x-h)²/# - (y-k)²/# = 1

parabola equation

y = a(x-h)² + k