trig packet

Question 1

convert from degrees to radian

Answer 1

degree x pi/180

Question 2

convert from radians to degrees

Answer 2

radian x 180/pi

Question 3

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

Answer 3

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

Question 4

Special Angles table

Answer 4

Question 5

Quadrantal Angles table

Answer 5

Question 6

state the number of revolutions for an angle

Answer 6

1. convert to radians
2. radians/2pi

Question 7

convert to decimal degree form

Answer 7

Ex: 152^o15’29”

152 + (15/60) + (20/3600) =

152.26^o

Question 8

decimal degree form

Answer 8

156.33^o

Question 9

DMS form

Answer 9

122^o25’51”

Question 10

convert to DMS form

Answer 10

Ex: 24.24^o

24o (.24•60)’ (.4*•60)”

24^o14’24”

*.4 is from (.24•60 = 14.4)

Question 11

1’ = ?

Answer 11

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

Question 12

1” = ?

Answer 12

one second = (1/60)(1’) = (1/3600)(1^o)

Question 13

quadrant rules

Answer 13

Question 14

terminal ray

Answer 14

the pipe cleaner

Question 15

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

Answer 15

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

Question 16

Find the exact value of sin/cos/tan x. do not use a calculator.

Answer 16

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

Question 17

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

Answer 17

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

Question 18

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

Answer 18

xmin = -2pi

xmax = 2pi

xscl = pi/2 (unless stated otherwise)

ymin = -5

ymax = 5

ycl = .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): normal period/b; max/min/amp same
• 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

Question 19

period

Answer 19

• 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

Question 20

amplitude

Answer 20

max - min

Question 21

vertical asymptotes

Answer 21

lines tht the graph approaches but doesn’t cross

Question 22

periodic

Answer 22

repeating

Ex: tan function

Question 23

csc, sec, cot

Answer 23

csc = 1/sin

sec = 1/cos

cot = 1/tan

Question 24

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

Answer 24

vertical asymptote

Question 25

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

Answer 25

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

Question 26

sine function: y = sin(x)

Answer 26

“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

Question 27

cosine function: y = cos(x)

Answer 27

also “wave”

amplitude = 1

period = 2pi

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

max = 1

min = -1

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

Question 28

tangent function: y = tan(x)

Answer 28

amplitude = none, go on forever in vertical directions

period = pi

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

Question 29

cotangent function: y = cot(x)

Answer 29

amplitude = none

period = pi

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

Question 30

relationship between tan graph & cot graph

Answer 30

The x-intercepts of the graph of y = tan(x) are the asymptotes of the graph of y = cot(x).

The asymptotes of the graph of y = tan(x) are the x-intercepts of the graph of y = cot(x).

Question 31

cosecant function: y = csc(x)

Answer 31

amplitude = none

period = 2pi

one cycle is between 0 & 2pi, with the center being @ pi/2

Question 32

relationship b/w sin graph & csc graph

Answer 32

The maximum values of y = sin x are minimum values of the positive sections of y = csc x.

The minimum values of y = sin x are the maximum values of the negative sections of y = csc x.

The x-intercepts of y = sin x are the asymptotes for y = csc x.

Question 33

secant function: y = sec(x)

Answer 33

amplitude = none

period = 2pi

one cycle occurs between -pi/2 and pi/2, with the center being at 0

Question 34

relationship b/w cos graph & sec graph

Answer 34

The maximum values of y = cos x are minimum values of the positive sections of y = sec x.

The minimum values of y = cos x are the maximum values of the negative sections of y = sec x.

 The x-intercepts of y = cos x are the asymptotes for  y = sec x.