PreCalc
0.0(0)
Studied by 1 person
Call Kai
Learn
Practice Test
Spaced Repetition
Match
Flashcards
Knowt PlayCard Sorting
1/27
Earn XP
Description and Tags
Last updated 1:39 PM on 6/14/23
Name | Mastery | Learn | Test | Matching | Spaced | Call with Kai |
|---|
No analytics yet
Send a link to your students to track their progress
28 Terms
1
New cards
Sin²θ + Cos²θ =
1
\
\
2
New cards
Cot²θ + 1 =
Csc²θ
3
New cards
Tan²θ + 1 =
Sec²θ
4
New cards
Cos (π/2 - θ) =
Sinθ
5
New cards
Cot (π/2 - θ) =
Tanθ
6
New cards
Csc (π/2 - θ) =
Secθ
7
New cards
Law of Sin
SinA/ a = SinB/b = SinC/c
8
New cards
Law of Cos
a² = b² + c² - 2bc(cosA)
9
New cards
Area of a triangle
Heron's formula
Area = √s(s-a)(s-b)(s-c)
s= ½(a+b+c)
OR
Area = ½bc(sinA)
\
Area = √s(s-a)(s-b)(s-c)
s= ½(a+b+c)
OR
Area = ½bc(sinA)
\
10
New cards
Reference angles
The distance from the terminal ray to the x-axis that is a positive acute angle
11
New cards
Three key points to graph a __**arcsin**__ or sin⁻¹ graph
(-1, -π/2)
(0, 0)
(1, π/2)
(0, 0)
(1, π/2)
12
New cards
Three key points to graph a __**arccos**__ or cos⁻¹ graph
(-1, π)
(0, π/2)
(1, 0)
(0, π/2)
(1, 0)
13
New cards
Three key points to graph a __**arctan**__ or tan⁻¹ graph
(-1, -π/4)
(0, 0)
(1, π/4)
(0, 0)
(1, π/4)
14
New cards
30° - 60° - 90° triangle
15
New cards
45° - 45° - 90° triangle
16
New cards
Coterminal angles
Angles with the same initial and terminal rays but different measures. Find them by doing …
θ +/- 360° OR θ +/- 2π
θ +/- 360° OR θ +/- 2π
17
New cards
Arc Lenght
S = r θ
S= length of intercepted arc
r = radious
θ = central angle in __radiants__
S= length of intercepted arc
r = radious
θ = central angle in __radiants__
18
New cards
Area of a Sector
A = ½ r² θ
19
New cards
How to find Asymptotes of y = a 1ⁿ /(x-h)ⁿⁿ + k
n = exponent of numerator
m = exponent of denominator
n = exponent of numerator
m = exponent of denominator
n = m
Horizontal asymptote: LC/LC
n > m
NO Horizontal asym
n < m
Horizontal asym: y= 0
n > m __**by 1**__
Slant asymp found by dividing numerator by denominator
Horizontal asymptote: LC/LC
n > m
NO Horizontal asym
n < m
Horizontal asym: y= 0
n > m __**by 1**__
Slant asymp found by dividing numerator by denominator
20
New cards
Loops? dimple? or cusp?
a
a>b = dimple
a=b = cusp (touch origin)
a>b = dimple
a=b = cusp (touch origin)
21
New cards
r= +/-asin nθ
r= +/-acos nθ
r= +/-acos nθ
a= max height of any rose petal
value of n= number of petals
* if odd # petals'= #petals=n. if even # of petals, #petals=2n
Sin is symmetric by the π/2 axis
Cos is symmetric by the polar axis (x=0)
value of n= number of petals
* if odd # petals'= #petals=n. if even # of petals, #petals=2n
Sin is symmetric by the π/2 axis
Cos is symmetric by the polar axis (x=0)
22
New cards
r = a +/- b sinθ
r = a +/-b cosθ
r = a +/-b cosθ
|a+b|= Max height
|a-b| = loop height
|a-b| = loop height
23
New cards
circle
r² = (x-h) **²**+ (y+k)²
24
New cards
Ellipse
(←→) (x+h)²/a² + (y+k)²/ b²
a= bigger #; determines if streched horiz or vertical
* d from center to vertecis
b = d from center to co-vertices
c = d from center to focci
c= √a² - b²
a= bigger #; determines if streched horiz or vertical
* d from center to vertecis
b = d from center to co-vertices
c = d from center to focci
c= √a² - b²
25
New cards
Parabola
vetical (x-h)² = 4p(y;k)
horz (y-k)² = 4p (x-h)
\
vertex (h,k)
focus 4p =
p=
\
horz (y-k)² = 4p (x-h)
\
vertex (h,k)
focus 4p =
p=
\
26
New cards
Hyperbola
direction deermined by which one is positive
vetical (y-k)² /a² - (x-h)² / b² = 1
\
a= d from vertices form center
c= d form goci to center
assymptote
y-k = +/- rise/run (x-h)
\
c= √a²+b²
vetical (y-k)² /a² - (x-h)² / b² = 1
\
a= d from vertices form center
c= d form goci to center
assymptote
y-k = +/- rise/run (x-h)
\
c= √a²+b²
27
New cards
Area of a sector
½r²θ
28
New cards
d of polar coordinates
√r₁² +r₂² -2r₁r₂cos (θ₂-θ₁)