How to convert from degrees to radians, and viceversa
Graphical
Movements
f(x)- original graph
Take your angle in degrees,
multiply it by pi/180 to get
radians. To convert from
radians to degrees, take
your angle in radians, multiply by 180/pi to get degrees.
SOHCAHTOA– The
acronym to
remember the trig
ratios
c f(x)- Vertical Stretch of c
(c– constant)
(1/c) f(x)- Vertical Shrink of c
f(x/c)- Horizontal Stretch of c
f(cx)- Horizontal Shrink of c
f(x-c)- Shift right c units
f(x+c)- Shift left c units
f(x)+c– Shift up c units
f(x)-c– Shift down c units
-f(x)- Reflection across x-axis
f(-x)- Reflection across y-axis
-f(-x)- Reflection across origin
How to convert from DMS to decimal
form and vice-versa.
Decimal -> DMS
The degrees are the numbers to the left
of the decimal point.
Take the number to the right of the
decimal, multiply it by 60.
The minutes are the numbers to the
left of the decimal.
Take the number to the right of the
decimal point, multiply that by 60 and
round.
Sin (theta) = Opp/Hyp
Cos (theta) = Adj/Hyp
Tan (theta) = sin(theta)/cos(theta)= Opp/
Adj
(Hypotenuse– side opposite to the right
angle).
http://www.mass.gov/mgis/llcoord.htm
csc (theta) = hyp/opp = 1/sin(theta)
This website gives a helpful example.
sec (theta) = hyp/adj = 1/cos(theta)
DMS -> Decimal
degrees + (minutes/60) +
(seconds/3600)
For example, to convert 42deg, 08min,
10sec into decimal format:
42 + (8/60) + (10/3600) = 42.1361
cot (theta) = adj/opp = 1/tan(theta)
a^2 + b^2 = c^2
Graphs of the 6 trig functions
tan (x)
csc (x)

Crosses x-axis at pi intervals


There are vertical asymptotes at each end of the
cycle. The asymptote that occurs at pi/2 repeats
every pi unit.
There are vertical asymptotes. The asymptote that
occurs at pi repeats every pi units.

Period: pi
Amplitude: none, graphs go on forever in vertical directions.
Period: 2*pi
Amplitude: none, graphs go on forever in vertical
directions.

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.

cot (x)



sin (x)
 Has amplitude = 1 and period = 2π.
 Crosses x-axis at pi intervals.
cos (x)
 Has amplitude = 1 and period = 2π.
 Crosses x-axis at pi/2 intervals.
http://regentsprep.org/Regents/math/algtrig/
ATT7/othergraphs.htm
http://www.intmath.com/trigonometric-graphs/1graphs-sine-cosine-amplitude.php
One cycle occurs between 0 and pi.
There are vertical asymptotes at each end of the
cycle. The asymptote that occurs at pi repeats
every pi units.
Period: pi
Amplitude: none, graphs go on forever in vertical directions

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).

The graphs of y = tan(x) and y = cot(x) have
the same x-values for y-values of 1 and -1.
sec (x)

There are vertical asymptotes. The asymptote that
occurs at pi/2 repeats every pi units.

Period: 2*pi
Amplitude: none, graphs go on forever in vertical
directions.

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.