The 6 Trigonometric Functions. Flashcards
If Theta = 0 degrees, Sin Theta =
0
If Theta = 0 degrees, Cos Theta=
1
If Theta = 0 degrees, Tan Theta=
0
If Theta = PI/2 or 90 degrees, Sin 90 degrees=
1
If Theta = PI/2 or 90 degrees, Cos 90 degrees=
0
If Theta = PI/2 or 90 degrees, Tan 90 degrees=
Undefined.
If Theta = PI or 180 degrees, Sin 180 degrees=
0
If Theta = PI or 180 degrees, Cos 180 degrees=
-1
If Theta = PI or 180 degrees, Tan 180 degrees=
0
If Theta = PI/4 or 45 degrees, Sin 45 degrees=
Root 2/2
If Theta = PI/4 or 45 degrees, Cos 45 degrees=
Root 2/2
If Theta = PI/4 or 45 degrees, Tan 45 degrees=
1
If Theta = PI/6 or 30 degrees, Sin 30 degrees=
1/2
If Theta = PI/6 or 30 degrees, Cos 30 degrees=
Root 3/2
If Theta = PI/6 or 30 degrees, Tan 30 degrees=
1/Root 3
If Theta = PI/3 or 60 degrees, Sin 60 degrees=
Root 3/2
If Theta = PI/3 or 60 degrees, Cos 60 degrees=
1/2
If Theta = PI/3 or 60 degrees, Tan 60 degrees=
Root 3
1 degree=
pi/180 radians
1 radian=
180/pi
Arc Length=
s=r theta
Area of a sector=
A=1/2 r (squared) theta.
Sin Theta=
y
Cos Theta=
x
Tan Theta=
y/x
Cosec Theta=
1/y
Sec Theta=
1/x
Cot Theta
x/y
What type of graph is this?
Sin
What type of graph is this?
Cos
What type of graph is this?
Cot
What type of graph is this?
Cosec
What type of graph is this?
Sec
What type of graph is this?
Tan
All Silver Tea Cups:
All is Quadrant I, _______ funtions are positive.
All!
All Silver Tea Cups:
Silver is Quadrant II and _______ and _______ functions are positive.
Sin and Cosecant!
All Silver Tea Cups:
Tea is Quadrant III and ______ and ______ functions are positive.
Tangent and Cotangent!
All Silver Tea Cups:
Cups is Quadrant IV and _____ and ______ functions are positive.
Cosecant and Secant!
What is the transformation?
y=f(x)+k
Vertically up by k units.
What is the transformation?
y=f(x)-k
Vertically down by k units.
What is the transformation?
y=f(x+h)
Horizontally left by h units.
What is the transformation?
y=f(x-h)
Horizontally right by h units.
What is the transformation?
y=f(x)
If a>1 vertically stretch.
If 0
What is the transformation?
y=f(a*x)
If a >1, horizontally compress.
If 0
What is the transformation?
y= -f(x)
Reflects about the x-axis.
What is the transformation?
y= f(-x)
Reflects about the y-axis.
In transformations, stretch=
Multiplication.
In transformations, Compress=
Division.
In transformations, Vertical=
On all y-coordinates.
In transformations, horizontal=
on all the x-coordinates.
Amplitude = I A I
All real numbers, no negatives.
Period =
T= 2pi/w
y=A sin w x
y=A cos w x
State the domain, range and period of a sin function f(x)=sin(x).
Domain= ARN
Range= [-1,1]
Period=2pi
State the domain, range and period of a cos function f(x)=cos(x).
Domain= ARN
Range= [-1,1]
Period=2pi
State the domain, range, period and vertical asymptootes of a tan function f(x)=tan(x).
Domain=all real numbers except pi/2 + k pi, k is an integer.
Range=ARN
Period=pi
Vertical asymptotes: x = pi/2 + k pi, where k is an integer.
State the domain, range, period and vertical asymptotes of a cot function f(x)=cot(x).
Domain: all real numbers except k pi, k is an integer.
Range: all real numbers
Period = pi
Vertical asymptotes: x = k pi, where k is an integer.
State the domain, range, period and vertical asymptotes of a sec function f(x)=sec(x).
Domain: all real numbers except pi/2 + k pi, n is an integer.
Range: (-infinity , -1] U [1 , +infinity)
Period = 2 pi
Vertical asymptotes: x = pi/2 + k pi, where k is an integer.
State the domain, range, period and vertical asymptotes of a csc function f(x)=csc(x).
Domain: all real numbers except k pi, k is an integer.
Range: (-infinity , -1] U [1 , +infinity)
Period = 2pi
Vertical asymptotes: x = k pi, where k is an integer.
