Chapter 6: Review Flashcards
180 degress =
pi radians
1 radian =
(180/pi)
1 degree =
(pi/180 radians)
Coterminal angles
angles that end in the same place
length of a circular arc
s=rΘ (Θ is in radians)
area of a sector
A=1/2r2Θ (Θ is in radians)
angular speed
w = Θ/t
linear speed
v = s/t
angle of elevation
looking up from horizon
angle of depression
looking down from horizon
sinΘ =
y/r
cosΘ =
x/r
tanΘ =
y/x
cscΘ =
r/y
cosΘ =
r/x
cotΘ =
x/y
reference angle
the acute angle formed by the terminal side of the angle and x-axis
area of a triangle
A=1/2bh (find height with trig)
domain and range of y=sinx
domain: [-pi/2, pi/2]
range: [-1, 1]
domain and range of y=cosx
domain: [0,pi]
range: [-1, 1]
y=tanx
domain: (-pi/2, pi/2)
range: all real numbers
law of sins
sina/a = sinb/b = sinc/c
cases for law of sins
ASA, AAS, SSA (only sometimes)
SSA (acute angle)
if a<h, no triangle
if a=h, one triangle
if a >= b, one triangle
if h<a<b, two triangles
SSA (obtuse angle)
if a<=b, no triangle
if a>b, one triangle
law of cosine
a2=b2 + c2 - 2bccosA
cases for law of cosines
SAS, SSS
Heron’s formula
A = √s(s-a)(s-b)(s-c)
semi perimeter
(a + b + c)/2
