ap precalc Flashcards
theta
s/r
sin theta
y/r
cos theta
x/r
tan theta
y/x
sin + cos + tan
pi/6
30
1/2
rad 3/2
rad 3/3
sin + cos + tan
pi/4
45
rad 2/2
rad 2/2
1
sin + cos + tan
pi/3
60
rad 3/2
1/2
rad 3
sin + cos + theta
pi/2
90
1
0
undefined
sin + cos + tan
2pi/3
120
rad 3/2
-1/2
-rad 3
sin + cos + tan
3pi/4
135
rad 2/2
-rad 2/2
-1
sin + cos + tan
5pi/6
150
1/2
-rad 3/2
-rad 3/3
sin + cos + tan
pi
180
0
-1
0
sin + cos + tan
7pi/6
210
-1/2
-rad 3/2
rad3/3
sin + cos + tan
5pi/4
225
-rad 2/2
-rad 2/2
1
sin + cos + tan
4pi/3
240
-rad 3/2
-1/2
1
sin + cos + tan
3pi/2
270
-1
0
undefined
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
