APPC pgs 7-8

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25 Terms

1
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logb b^x=

x

2
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b^logb x=

x

3
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log 1

0

4
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log 10

1

5
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log 10^x

x

6
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10^log x

x

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ln 1

0

8
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ln e

1

9
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ln e^x

x

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e^ln x

x

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logb xy=

logb x+logb y

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logb x/y=

logb x-logb y

13
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logb x^p=

p logb x

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Change of Base Formula

for any positive real numbers a, b, and x, a not 1, b not 1

logb x= loga x/loga b

15
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Radian

1 radius

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To convert radians to degrees

180/pi

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To convert degress to radians

pi/180

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Length of a circular arc

𝑠 = 𝑟𝜃

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Linear Speed

arc length/time = s/t

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Angular Speed

central angle/time = 𝜃/t

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sin 𝜃=

opp/hyp and y/r and 1/csc 𝜃

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cos 𝜃=

adj/hyp and x/r and 1/sec 𝜃

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tan 𝜃=

opp/adj and y/x and 1/cot 𝜃

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cot 𝜃=

adj/opp and x/y and 1/tan 𝜃

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csc 𝜃=

hyp/opp and r/y and 1/sin 𝜃