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Flashcards in Finals Deck (227)
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1

degrees → radian

degree • pi/180

2

radians → degree

radian • 180/pi

3

evaluate sin x, cos x, and tan x for a value x

  1. if necessary, convert x to degrees
  2. Check what quadrant it's in
  3. Do whatever the quadrant says to do
  4. Use special/quadrantal angles tables to solve

4

special angles table

5

quadrantal angles table

y = sin x graph → 0 1 0 -1 0

y = cos x graph → 1 0 -1 0 1

tan x = sinx/cosx

6

state the number of revolutions for an angle

1. convert to radians

2. radians/2pi

7

convert to decimal degree form

Ex: 152o15'29"

152 + (15/60) + (20/3600) = 

152.26o

8

decimal degree form

156.33o

9

DMS form

122o25'51"

10

convert to DMS form

Ex: 24.240

24(.24*•60)' (.4**•60)"

24o14'24"

*.24 is from 24.24

**.4 is from (.24•60 = 14.4)

11

1' = ?

one minute = (1/60)(1o)

12

1" = ?

one second = (1/60)(1') = (1/3600)(1o)

13

quadrant rules

14

terminal ray

the pipe cleaner

15

in which quadrant does the terminal side of each angle lie when it is in standard position?

  1. convert to degrees
  2. if negative, + 360; if over 360, - 360
  3. find which quadrant it's in

16

find the exact value of sin/cos/tan x. no calculator.

  1. if radians, convert to degrees
  2. use quick charts

 

17

use a calc to approximate sin/cos/tan x to four decimal places

  • if degree, change calc to Degree mode
  • if radians, change calc to Radians mode

18

sketch w/out a calculator a sin/cos/tan curve

xmin = -2pi

xmax = 2pi

xscl = pi/2 (unless stated otherwise)

ymin = -5

ymax = 5

yscl = .5

sin, cos

  • if y = c + cos(x) → period & amplitude same; c = pos moves max/min up, c = neg moves max/min down
  • if y = a sin(x) → period same; move max to a
  • if y = sin(bx) → max/min/amp same; normal period/b
  • if y = sin(x + b) → if b = pos, move left; if b = neg, move right

tan, cot, sec, csc - no ampl/min/max

  • y = c + tan(x) → if c = pos, move up; c = neg, move down (easier to just move x-int's)
  • y = a csc(x) → move min/max's to a
    • y = cot(bx) → period/b

19

period

  • for sin, cos curves → the shortest distance along the x-axis over which the curve has one complete up-and-down cycle
  • for tan, distance b/w consecutive x-intercepts

 

20

amplitude

max - min

21

vertical asymptotes

lines that the graph approaches but doesn't cross

22

periodic

repeating

Ex: tan function

23

csc, sec, cot

csc = 1/sin

sec = 1/cos

cot = 1/tan

24

what happens to y = csc(x) whenever y = sin(x) touches the x-axis?

vertical asymptote

25

why are y = sin(x) and y = csc(x) tangent whenver x is a multiple of x

they r reciprocals, so csc's max is at sin's min, and csc's min is at sin's max

26

sine function: y = sin(x)

"wave"

amplitude - 1

period - 2pi

frequency = 1 cycle in 2pi radians (1/2pi)

max - 1

min - (-1)

one cycle occurs between 0 and 2pi with x-int @ pi

27

cosine function: y = cos(x)

also "wave"

amplitude = 1

period = 2pi

period = 2pi

frequency = 1 cycle in 2pi radians (1/2pi)

max = 1

min = -1

one cycle occurs b/w 0 & 2pi w/ x-int's @ pi/2 & 3pi/2

28

tangent function: y = tan(x)

amplitude = none, go on forever in vertical directions

period = pi

one cycle occurs b/w -pi/2 and pi/2 (x-int = 0)

 

29

cotangent function: y = cot(x)

amplitude = none

period = pi

one cycle occurs b/w 0 and pi (x-int pi/2)

30

relationship b/w tan & cot graphs

the x-int's of y = tan(x) are the asymptotes of y = cot(x)

and vice versa