Transcript Right Triangle Trigonometry

Graphs of the Other
Trigonometric Functions
Section 4.6
Objectives
• Determine the period and phase shift of the
graph of a tangent, cotangent, secant, or
cosecant function given an equation.
• Match a graph to its equation.
• Determine the domain, range, asymptotes,
period and phase shift of the graph of a
tangent, cotangent, secant, or cosecant
function given a graph.
• Draw the graphs of a tangent, cotangent,
secant, or cosecant function.
• Determine if the sine, cosine, tangent,
cotangent, secant, or cosecant functions are
even, odd, or neither.
General Function
f (x )  A tan( Bx  C )  D
f (x )  A cot( Bx  C )  D

B
C
B
 period
 phase shift
Graph the function tan(x) on the
interval [―2π, 2π]
What is the period?
What is the phase shift?
What is the domain?
What is the range?
Are there any asymptotes? If yes, what are
they?
Is the function even, odd or neither?
Graph the function cot(x) on the
interval [―2π, 2π]
What is the period?
What is the phase shift?
What is the domain?
What is the range?
Are there any asymptotes? If yes, what are
they?
Is the function even, odd or neither?
General Function
f (x )  A sec( Bx  C )  D
f (x )  A csc( Bx  C )  D
2
 period
B
C
B
 phase shift
Graph the function sec(x) on the
interval [―2π, 2π]
What is the period?
What is the phase shift?
What is the domain?
What is the range?
Are there any asymptotes? If yes, what are
they?
Is the function even, odd or neither?
Graph the function csc(x) on the
interval [―2π, 2π]
What is the period?
What is the phase shift?
What is the domain?
What is the range?
Are there any asymptotes? If yes, what are
they?
Is the function even, odd or neither?
Graph
x

y  2 tan  
4
Graph
1
y  cot x 
2
Graph
y  2 csc x 
Graph
y  tan x   