9.1-9.4

Question 1

degrees to radians

Answer 1

1 degree = pi/180

Question 2

30, 45, 60, 90, 180, 270, 360 deg to radians

Answer 2

pi/6, /4, /3, /2, pi, 3pi/2, 2pi

Question 3

arc length formula

Answer 3

S=r × thanos
r is radius
thanos is central angle of S in RADIANS

Question 4

area of sector of a circle formula

Answer 4

A=½r² × thanos
thanos in RADIANS

Question 5

linear speed formula

Answer 5

V=s/t
s is length of arc
t is time

Question 6

angular speed formula

Answer 6

w=thanos/t
thanos in RADIANS

Question 7

all trig values

Question 8

x and y who’s who in trig formulas

Answer 8

x is adj y is opp

Question 9

signs of trig is each quadrant

Answer 9

all + in I, sin in II, tan in III, cos in IV
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Question 10

Pythagorean identities (3)

Answer 10

sin²+cos²=1, 1+tan²=sec², 1+cot²=csc²

Question 11

range of trig functions

Answer 11

sin and cos AV<=1, tan and cot all real numbers, csc and sec AV >=1

Question 12

grade resistance formula

Answer 12

R=Wsin thanos
W is weight
thanos angle of grade

Question 13

30 60 90 and 45 45 90 triangles

Answer 13

1 sqrt3 2, w/ 1 between 60 and 90 sqrt3 between 30 and 90; 1 1 sqrt2

Question 14

cofunction identities

Answer 14

sinA=cosB, tanA=cotB, cscA=secB

Question 15

reference angle

Answer 15

from terminal side to x- axis

Question 16

special right triangles in a unit circle

Answer 16

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

Question 17

angle measure in unit circle

Answer 17

thanos equals s in RADIANS
adapted from arc formula

Question 18

circular functions (sin and cos)

Answer 18

sin=y, cos=x, hyp=1

Question 19

sin: period, points

Answer 19

2pi/b, passes through origin and up for pi/2

Question 20

cos: period, points

Answer 20

2pi/b, y=1 when x=0

Question 21

label y=c+asin(b(x-d))

Answer 21

c is vertical shift, |a| is amplitude, any sign reflects across x axis, b is for period, d is phase shift

Question 22

finding points of cos or sin using interval

Answer 22

avg of interval coordinates is midpoint, avg of mid and endpoints is other 2 points

Question 23

inequality to find interval using period and phase shift (for sin and cos)

Answer 23

0<=b(x-d)<=2pi, solve so x is in the middle and the ends are your endpoints

Question 24

sec asymptotes

Answer 24

pi/2, 3pi/2, x intercepts of cos

Question 25

csc asymptotes

Answer 25

0, pi, 2pi, x intercepts of sin

Question 26

tan and cot zeroes and functions

Answer 26

tan: zeroes same as sin, positive slant; cot: zeroes same as cos, negative slant
note: 2 asympt = 1 period

Question 27

tan and cot period

Answer 27

pi/b

Question 28

how to find asymptotes of tan and cot

Answer 28

solve bx=pi/2 and bx=-pi/2 for tan, and bx=0 and bx=pi for cot

Question 29

unit circle special right triangles

Answer 29

sqrt2/2, sqrt2/2, 1; and sqrt3/2, 1/2, 1

Question 30

sin and cos zeroes

Answer 30

pi, 2pi and pi/2, 3pi/2

Question 31

how to find interval to graph son and cos

Answer 31

0<=b(x-d)<=2pi solve for x

divide for midpoints

Question 32

period of cos sin tan

Answer 32

2pi, pi for tan

Question 33

tan and cot zeroes

Answer 33

pi etc, pi/2 etc
same as sin, same as cos

Question 34

how to find asymptotes of tan and cot

Answer 34

tan: b(x-d)= -pi/2 and b(x-d)= pi/2
cot: b(x-d)=0 and b(x-d)=pi