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
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
Special Angles table
Quadrantal Angles table
state the number of revolutions for an angle
1. convert to radians
2. radians/2pi
convert to decimal degree form
Ex: 152^{o}15'29"
152 + (15/60) + (20/3600) =
152.26^{o}
decimal degree form
156.33^{o}
DMS form
122^{o}25'51"
convert to DMS form
Ex: 24.24^{o}
24o (.24•60)' (.4*•60)"
24^{o}14'24"
*.4 is from (.24•60 = 14.4)
1' = ?
one minute = (1/60)(1^{o})
1" = ?
one second = (1/60)(1') = (1/3600)(1^{o})
quadrant rules
terminal ray
the pipe cleaner
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
Find the exact value of sin/cos/tan x. do not use a calculator.
1. if radians, convert to degrees
2. 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 xint'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 xaxis over which the curve has one complete upanddown cycle

for tan, distance b/w consecutive xintercepts
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 xaxis?
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 xint @ 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/ xint'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 (xint = 0)
cotangent function: y = cot(x)
amplitude = none
period = pi
one cycle occurs b/w  and pi (xint pi/2)
relationship between tan graph & cot graph
The xintercepts 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 xintercepts of the graph of y = cot(x).