trig packet Flashcards
convert from degrees to radian
degree x pi/180
convert from radians to degrees
radian x 180/pi
evaluate sin x, cos x, and tan x for a value x
- if necessary, convert x to degrees
- check what quadrant it’s in
- do whatever the quadrant says to do
- use special/quadrantal angles tables to solve
Special Angles table
Quadrantal Angles table
state the number of revolutions for an angle
- convert to radians
- radians/2pi
convert to decimal degree form
Ex: 152o15’29”
152 + (15/60) + (20/3600) =
152.26o
decimal degree form
156.33o
DMS form
122o25’51”
convert to DMS form
Ex: 24.24o
24o (.24•60)’ (.4*•60)”
24o14’24”
*.4 is from (.24•60 = 14.4)
1’ = ?
one minute = (1/60)(1o)
1” = ?
one second = (1/60)(1’) = (1/3600)(1o)
quadrant rules
terminal ray
the pipe cleaner
In which quadrant does the terminal side of each angle lie when it is in standard position?
- convert to degrees
- if negative, + 360; if over 360, - 360
- find which quadrant it’s in
Find the exact value of sin/cos/tan x. do not use a calculator.
- if radians, convert to degrees
- use quick charts
use a calculator to approximate sin/cos/tan x to four decimal places
- if degree, change calc to Degree mode
- if radians, change calc to Radians mode
Sketch w/out a calculator a sin/cos/tan curve
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
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
amplitude
max - min
vertical asymptotes
lines tht the graph approaches but doesn’t cross
periodic
repeating
Ex: tan function
csc, sec, cot
csc = 1/sin
sec = 1/cos
cot = 1/tan
what happens to y = csc(x) whenever y = sin(x) touches the x-axis?
vertical asymptote
why are y = sin(x) & 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’ max
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
cosine function: y = cos(x)
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
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)
cotangent function: y = cot(x)
amplitude = none
period = pi
one cycle occurs b/w - and pi (x-int pi/2)
relationship between tan graph & cot graph
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).
cosecant function: y = csc(x)
amplitude = none
period = 2pi
one cycle is between 0 & 2pi, with the center being @ pi/2
relationship b/w sin graph & csc graph
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.
secant function: y = sec(x)
amplitude = none
period = 2pi
one cycle occurs between -pi/2 and pi/2, with the center being at 0
relationship b/w cos graph & sec graph
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.
