AP Calculus AB Flashcards

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38 Terms

1

Pythagorean Identity #1

sin²θ + cos²θ = 1

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2

Pythagorean Identity #2 (divide by sin²)

1 + cot²θ = csc²θ

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3

Pythagorean Identity #3 (divide by cos²)

tan²θ + 1 = sec²θ

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4

Double Angle Identity #1

sin2θ = 2sinθcosθ

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5

Double Angle Identity #2

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

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6

Double Angle Identity #3

tan2θ = 2tanθ/1 - tan²θ

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7

lne = ?

1

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8

ln 1 = ?

0

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9

log 10 = ?

1

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10

log 1 = ?

0

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11

lognn = ?

1

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12

logn1 = ?

0

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13

logAB = ?

BlogA

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14

log (A B) = ?

logA + logB

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15

(x,y) in terms of cos and sin

(cosθ, sinθ)

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16

tan = ?

sinθ/cosθ

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17

cotθ = ?

cosθ/sinθ

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18

IVT

if a function is continuous on [a, b], and if k is any number between f(a) and f(b), then there must be a value in [a,b] such that f = k

end points aren’t equal, closed interval, continuous

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19

definition of derivatives

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20

point slope formula

y-y1 = m(x-x1)

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21

d/dx

derivative

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22

d/dx axn

a * nxn-1

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23

d/dx sinx

cosx

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24

d/dx secx

secx * tanx

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25

d/dx a (a is a constant)

0

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26

d/dx cosx

-sinx

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27

d/dx cscx

-cscx * cotx

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28

d/dx cotx

-csc²x

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29

d/dx tanx

sec²x

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30

d/dx lnx

1/x

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31

logex

lnx

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32

d/dx logax

1/lna * x

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33

d/dx ex

ex

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34

d/dx ax

lna * ax

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35

product rule

d/dx f(x) * s(x) = (f(x))(s(x)) + (f(x))(s(x))

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36

f(x) = sinx * cosx

f(x) = cos2x

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37

g(x) = cotx

g(x) = -csc²x

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38

quotient rule

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