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math.. > ap precalc > Flashcards

ap precalc Flashcards

1
Q

theta

A

s/r

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2
Q

sin theta

A

y/r

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3
Q

cos theta

A

x/r

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4
Q

tan theta

A

y/x

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5
Q

sin + cos + tan
pi/6
30

A

1/2
rad 3/2
rad 3/3

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6
Q

sin + cos + tan
pi/4
45

A

rad 2/2
rad 2/2
1

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7
Q

sin + cos + tan
pi/3
60

A

rad 3/2
1/2
rad 3

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8
Q

sin + cos + theta
pi/2
90

A

1
0
undefined

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9
Q

sin + cos + tan
2pi/3
120

A

rad 3/2
-1/2
-rad 3

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10
Q

sin + cos + tan
3pi/4
135

A

rad 2/2
-rad 2/2
-1

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11
Q

sin + cos + tan
5pi/6
150

A

1/2
-rad 3/2
-rad 3/3

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12
Q

sin + cos + tan
pi
180

A

0
-1
0

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13
Q

sin + cos + tan
7pi/6
210

A

-1/2
-rad 3/2
rad3/3

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14
Q

sin + cos + tan
5pi/4
225

A

-rad 2/2
-rad 2/2
1

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15
Q

sin + cos + tan
4pi/3
240

A

-rad 3/2
-1/2
1

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16
Q

sin + cos + tan
3pi/2
270

A

-1
0
undefined

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17
Q

sin + cos + tan
5pi/3
300

A

-1/2
rad 3/2
rad 3

18
Q

sin + cos + tan
7pi/4
315

A

-rad 2/2
rad 2/2
-1

19
Q

sin + cos + tan
11pi/6
330

A

-rad 3/2
1/2
-rad 3/3

20
Q

sin + cos + tan
2pi
360

A

0
1
0

21
Q

asin(b(x+c))+d

A

a: amplitude, vertical dilation
b: helps define period, horizontal dilation
period - 2pi/b
c: horizontal shift / phase shift
d: vertical shift

22
Q

inverse trig functions

A

sin^-1 (x) = angle
input is y coordinate

23
Q

pythagorean trig identities

A

cos^2 theta + sin^2 theta = 1
1+ tan^2 theta = sec^2 theta
cot^2 theta + 1 = csc ^2 theta

24
Q

double angle trig identity

A

sin 2 theta =
2(sin theta)(cos theta)

cos 2 theta =
2 cos^2 theta -1
1- sin^2 theta
cos^2 theta - sin^2 theta

tan 2 theta = (2 tan theta)/ (1 - tan2 theta)

25
Q

half angle trig identities

A

sin (A/2) =
+- rad (1-cos theta)/2

cos (A/2) =
+- rad (1+cos theta)/2

tan (A/2) =
(1- cos theta) / (sin theta)
(sin theta)/ (1+ cos theta)

26
Q

addition and subtraction trig identities

A

sin (A+ B)
sinAcosB+cosAsinN
switch with subtraction sign for subtraction

cos (A+B)
cosAcosB-sinAsinB
switch with addition sign for subtraction

tan (A+B)
(tanA+tanB)/(1-tanAtanB)
switch signs for subtraction

27
Q

log laws

A

loga (mn) = loga m+ loga n
loga (a) = 1
loga (m/n) = loga m- loga n
loga (m)^n = n loga m

CHANGING BASE
loga m = logp (m/logp a)
* p is new base

RECIPROCALS
loga m = 1/ loga m

28
Q

exponential laws

A

a^m x a^n = a^ m+n
a^m / a^n = a^ m-n
(a^m)^n = a^ m*n

29
Q

area of a triangle

A

1/2 absinC

30
Q

law of sin

A

a/ sinA = b/ sinB = c/ sinC

31
Q

area of a parallelogram

A

absinC

32
Q

law of cos

A

a^2 = b^2 + c^2 -2bc cosA

33
Q

polar graphing circles

A

acos x
asin x

34
Q

polar graphing limacons

A

a+bcosC
a+bsinC

types:
inner loops
cardioids
dimples
no dimple no inner loop

35
Q

limacon : inner loop

A

a/b <1
a+b = max value
a-b = length of inner loop

36
Q

cardiod

A

a/b= 1
heart shape
a+b = max value
touches origin

37
Q

dimple

A

1 < a/b < 2
a+b = max value
a-b = distance between dimple and origin
“small dent in circle”

38
Q

no dimple no inner loop

A

a/b> 2
a circle with a “flat” side
a+b = max value
a-b = distance from flat side to origin

39
Q

limacon orientation

A

cos +
positive x axis

cos -
negative x axis

sin +
positive y axis

sin -
negative y axis

40
Q

rose curves

A

acos nx
asin nx
# of petals depends on n
n is odd - n petals
n is even - 2n petals
length of a petal = a

differentiate between sin and cos:
sin rose curves NEVER have petals on the X AXIS

41
Q

polar coordinates

A

(r, theta)
|r| = radius
(-r, theta) reflects across origin

42
Q

converting between rectangular and polar

A

rectangular -> polar
x^2 + y^2 = r^2
tan theta = y/x

polar -> rectangular
x= rcos theta
y= rsin theta

math.. (3 decks)

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