9.1-9.4 Flashcards
degrees to radians
1 degree = pi/180
30, 45, 60, 90, 180, 270, 360 deg to radians
pi/6, /4, /3, /2, pi, 3pi/2, 2pi
arc length formula
S=r × thanos
r is radius
thanos is central angle of S in RADIANS
area of sector of a circle formula
A=½r² × thanos
thanos in RADIANS
linear speed formula
V=s/t
s is length of arc
t is time
angular speed formula
w=thanos/t
thanos in RADIANS
all trig values
x and y who’s who in trig formulas
x is adj y is opp
signs of trig is each quadrant
all + in I, sin in II, tan in III, cos in IV
ALL Students Take Calculus
Pythagorean identities (3)
sin²+cos²=1, 1+tan²=sec², 1+cot²=csc²
range of trig functions
sin and cos AV<=1, tan and cot all real numbers, csc and sec AV >=1
grade resistance formula
R=Wsin thanos
W is weight
thanos angle of grade
30 60 90 and 45 45 90 triangles
1 sqrt3 2, w/ 1 between 60 and 90 sqrt3 between 30 and 90; 1 1 sqrt2
cofunction identities
sinA=cosB, tanA=cotB, cscA=secB
reference angle
from terminal side to x- axis
special right triangles in a unit circle
45 45 90 is sqrt2/2 sqrt2/2 1, 60 30 90 or pi/3 pi/6 pi/2 is 1 sqrt3/2 1/2
angle measure in unit circle
thanos equals s in RADIANS
adapted from arc formula
circular functions (sin and cos)
sin=y, cos=x, hyp=1
sin: period, points
2pi/b, passes through origin and up for pi/2
cos: period, points
2pi/b, y=1 when x=0
label y=c+asin(b(x-d))
c is vertical shift, |a| is amplitude, any sign reflects across x axis, b is for period, d is phase shift
finding points of cos or sin using interval
avg of interval coordinates is midpoint, avg of mid and endpoints is other 2 points
inequality to find interval using period and phase shift (for sin and cos)
0<=b(x-d)<=2pi, solve so x is in the middle and the ends are your endpoints
sec asymptotes
pi/2, 3pi/2, x intercepts of cos
csc asymptotes
0, pi, 2pi, x intercepts of sin
tan and cot zeroes and functions
tan: zeroes same as sin, positive slant; cot: zeroes same as cos, negative slant
note: 2 asympt = 1 period
tan and cot period
pi/b
how to find asymptotes of tan and cot
solve bx=pi/2 and bx=-pi/2 for tan, and bx=0 and bx=pi for cot
unit circle special right triangles
sqrt2/2, sqrt2/2, 1; and sqrt3/2, 1/2, 1
sin and cos zeroes
pi, 2pi and pi/2, 3pi/2
how to find interval to graph son and cos
0<=b(x-d)<=2pi solve for x
divide for midpoints
period of cos sin tan
2pi, pi for tan
tan and cot zeroes
pi etc, pi/2 etc
same as sin, same as cos
how to find asymptotes of tan and cot
tan: b(x-d)= -pi/2 and b(x-d)= pi/2
cot: b(x-d)=0 and b(x-d)=pi
