ap precalc Flashcards by duo .

theta

s/r

How well did you know this?

Not at all

Perfectly

sin theta

y/r

How well did you know this?

Not at all

Perfectly

cos theta

x/r

How well did you know this?

Not at all

Perfectly

tan theta

y/x

How well did you know this?

Not at all

Perfectly

sin + cos + tan
pi/6
30

1/2
rad 3/2
rad 3/3

How well did you know this?

Not at all

Perfectly

sin + cos + tan
pi/4
45

rad 2/2
rad 2/2
1

How well did you know this?

Not at all

Perfectly

sin + cos + tan
pi/3
60

rad 3/2
1/2
rad 3

How well did you know this?

Not at all

Perfectly

sin + cos + theta
pi/2
90

1
0
undefined

How well did you know this?

Not at all

Perfectly

sin + cos + tan
2pi/3
120

rad 3/2
-1/2
-rad 3

How well did you know this?

Not at all

Perfectly

sin + cos + tan
3pi/4
135

rad 2/2
-rad 2/2
-1

How well did you know this?

Not at all

Perfectly

sin + cos + tan
5pi/6
150

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

How well did you know this?

Not at all

Perfectly

sin + cos + tan
pi
180

0
-1
0

How well did you know this?

Not at all

Perfectly

sin + cos + tan
7pi/6
210

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

How well did you know this?

Not at all

Perfectly

sin + cos + tan
5pi/4
225

-rad 2/2
-rad 2/2
1

How well did you know this?

Not at all

Perfectly

sin + cos + tan
4pi/3
240

-rad 3/2
-1/2
1

How well did you know this?

Not at all

Perfectly

sin + cos + tan
3pi/2
270

-1
0
undefined

How well did you know this?

Not at all

Perfectly

sin + cos + tan
5pi/3
300

-1/2
rad 3/2
rad 3

sin + cos + tan
7pi/4
315

-rad 2/2
rad 2/2
-1

sin + cos + tan
11pi/6
330

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

sin + cos + tan
2pi
360

0
1
0

asin(b(x+c))+d

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

inverse trig functions

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

pythagorean trig identities

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

double angle trig identity

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)

half angle trig identities

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)

addition and subtraction trig identities

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

log laws

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

exponential laws

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

area of a triangle

1/2 absinC

law of sin

a/ sinA = b/ sinB = c/ sinC

area of a parallelogram

absinC

law of cos

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

polar graphing circles

acos x asin x

polar graphing limacons

a+bcosC a+bsinC types: inner loops cardioids dimples no dimple no inner loop

limacon : inner loop

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

cardiod

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

dimple

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

no dimple no inner loop

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

limacon orientation

cos + positive x axis cos - negative x axis sin + positive y axis sin - negative y axis

rose curves

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

polar coordinates

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

converting between rectangular and polar

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