3.4-3.8

Question 1

axis’ of sin and cos graphs

Answer 1

x - angle
y - output

Question 2

regularities of a sin graph

Answer 2

origin (0,0)
max @ 1
amp of 1
midline @ y=0
period 2pi

Question 3

midline

Answer 3

halfway between max and min

Question 4

amplitude

Answer 4

distance from midline to max/min

Question 5

period

Answer 5

length of one complete cycle

Question 6

frequency

Answer 6

reciprocal of the period

Question 7

regularities of a cos graph

Answer 7

origin (0,1)
max @ 1
amp of 1
midline @ y=0
period 2pi

Question 8

sinusoidal function

Answer 8

any function involving the transformations of a sin (or cos)

Question 9

cos(theta)=

Answer 9

sin(theta + pi/2)

Question 10

transformations

Answer 10

midline, vertical translation
amplitude, vertical dilation
period, horizontal dilation

Question 11

vertical dilations: stretches vs. compressions

Answer 11

a>1, stretch
0<a<1 compression

Question 12

to find b (horizontal dilation)

Answer 12

set given period = 2pi/b

Question 13

a

Answer 13

vertical dilation (amplitude)

Question 14

d

Answer 14

vertical translation (midline)

Question 15

b

Answer 15

horizontal dilation by a factor of 1/b

Question 16

phase shift of a sinusoidal function

Answer 16

(x+c)
acts opposite how you might think

Question 17

to find c

Answer 17

see translation from origin, also plug points in to see what works!
b(max+c)=regular x max value

Question 18

sinusoidal function form

Answer 18

f(theta)=asin(b(theta+c))+d

Question 19

regular max x values for sin and cos graphs

Answer 19

sin:pi/2
cos:0

Question 20

d (midline) calculation

Answer 20

max+min/2

Question 21

a (amplitude) calcuation

Answer 21

max-midline or midine-min

Question 22

set iterations to

Answer 22

16 (for best accuracy)

Question 23

sinusoidal regression

Answer 23

enter 16 for iteration, enter data, leave period empty or put given value, calculate

Question 24

tangent of an angle is also…

Answer 24

the slope of the terminal ray
ratio of the angel’s sine to its cosine values

Question 25

vertical ray’s slope is…

Answer 25

undefined

Question 26

horizontal ray’s slope is…

Answer 26

0

Question 27

positive vs. negative slope quadrants

Answer 27

1: +
between: undefined
2: -
between: 0
3: +
between: undefined
4: -
between: 0

Question 28

vertical asymptotes of tangents

Answer 28

each half-turn around a circle will create another vertical asymptote
pi/2 and 3pi/2 = regular vertical asymptotes

Question 29

regular function of a tangent function

Answer 29

f(theta)=atan(b(theta+c))+d

Question 30

regular values for a tangent

Answer 30

period = pi
no amplitude, no midline
VAs: pi/2+pik
origin @ (0,0)

Question 31

b for tangents

Answer 31

period=pi/b

Question 32

c for tangents

Answer 32

phase shift
-c right
+c left

Question 33

VAs for tangents

Answer 33

pi/2 or 3pi/2 + period*k

Question 34

coordinates of unit circle

Answer 34

0/2pi - (1,0)
pi/6 - (sqrt(3)/2,1/2)
pi/2 - (sqrt(2)/2, sqrt(2)/2)
pi/3 - (1/2, sqrt(3)/2)
pi/2 - (0,1)
pi - (-1, 0)
3pi/2 - (0, -1)