AP Calc Mem Quiz (1-2)

Log_b(A ⋅ C) =

Log_bA + Log_bC

LogbA^B =

BLog_bA

(x,y) for cos and sine

(cosθ,sinθ)

lne =

1

ln1 =

0

log10 =

1

log 1 =

0

log_n1 =

0

lne^x =

x

e^lnx =

x

tan =

sinθ/cosθ

cotθ =

cosθ/sinθ

xⁿ ⋅ x^m =

x^n+m

(x^m)ⁿ =

x^mn

x⁰ =

1

EX: sin π/3 =

√3/2

EX: cos 3π/4

-√2/2

EX: tan 11π/6 =

-1/√3 = -√3/3

EX: cot 5π/4 =

1

Pythagorean Identity #1

sin²θ + cos²θ = 1

Pythagorean Identity #2 (divide by sin²)

1 + cot²θ = csc²θ

Pythagorean Identity #3 (divide by cos²)

tan²θ + 1 = sec²θ

Double Angle Identity #1

sin2θ = 2sinθcosθ

Double Angle Identity #2

cos2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

Double Angle Identity #3

tan2θ = 2tanθ/1 - tan²θ

log_b(E/F)

log_bE - log_bF

secθ =

1/cosθ

cscθ=

1/sinθ

d/dx xⁿ

nx^n-1

d/dx c

0

d/dx lnx

1/x

d/dx x

1

d/dx e^x

e^x

d/dx a^x

ln(a) * a^x

d/dx sinx

cosx

d/dx cosx

-sinx

d/dx tanx

sec²x

d/dx cotx

-csc²x

d/dx secx

secxtanx

d/dx csc

-cscxcotx

d/dx arcsinx

1/√1-x²

d/dx arccosx

-1/√1-x²

d/dx arctanx

1/1+x²

d/dx arccot

-1/1+x²

d/dx arcsecx

1/|x|√x²-1

d/dx arccscx

-1/|x|√x²-1

Quotient Rule d/dx t(x)/b(x)

(b(x))(t’(x)) - (t(x))(b’(x)) / (b(x))2