Section 7-5 The Other Trigonometric Functions
Objective: To find the values of: the tangent, cotangent, secant, and
cosecant functions and to sketch the functions’
graphs.
FILL IN THE TABLE BELOWQuadrant
I
II
III
IV
Topics to know for today’s lesson
State the reciprocal of each:
Divide each. Leave answers in exact form.
We can define other trig functions in terms of (x,y).
name Abbreviation definition
tangent of tan
cotangent of
cot
secant of sec
cosecant of csc
tan y
x
sec r
x
cot x
y
y
rcsc
Reciprocals
cotcos
sin
tan
sin
cos
cos
1sec
cscsin
1
cottan
1
Fill in the table below with appropriate signsQ1 Q2 Q3 Q4
tan
cot
sec
csc
Fill in the table below with appropriate signsQ1 Q2 Q3 Q4
tan + - + -
cot + - + -
sec + - - +
csc + + - -
Positive Negative
Find the value of each; round to the nearest
hunderdths
1. )
HINT: Make sure to use the proper mode.
RestrictionsFunction Definition restriction
Why do the restrictions matter
The value of the function on the calculator
The graph of the function.
Find the value of each expression to four significant digits.
A.) tan 203°
B.) cot 165°
C.) csc (-1)
D.) sec 11
Hint:
Express each in terms of reference angle:
1) csc 285°2) sec 749°3) csc -245°4) sec 5) csc
Sec 7.5 day 2Express each of the
following in terms of a reference angle.
Tangent and secant functions on unit circle.
BD represents themeasure of sec
DC represents themeasure of tan
D
EB C
A
Cotangent and cosecant on the unit circle
BF is the csc GF is cot
FG
EB C
A
Graph
-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π
-9-8-7-6-5-4-3-2-1
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x
ytan θ
θin radians
What you should know about
1) Domain2) Range3) Period4) Asymptotes5) The connection between the
asymptotes and the definition of the .6) The connection between the
asymptotes and the values on the UC
Graph fundamental period
-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π
-9-8-7-6-5-4-3-2-1
123456789
x
ytan θ
θin radians
Graph
-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π
-9-8-7-6-5-4-3-2-1
123456789
x
y
θ radians
Sec θ why can’t be between -1 and 1?
What you should know about
1) Domain2) Range3) Period4) Asymptotes5) The connection between the
asymptotes and the definition of the .6) The connection between the
asymptotes and the values on the UC
Graph for one period
-3π -5π/2 -2π -3π/2 -π -π/2 π/2 π 3π/2 2π 5π/2 3π
-9-8-7-6-5-4-3-2-1
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x
y
If q was in degrees:
How would each graph be different?
How would each graph be the same?
What would the period and amplitude be?
Given θ is a second-quadrant angle If , find the values of the other five
trigonometric functions.
Homeworkwritten exercise sec 7.5
DAY 1: # 1-9 allDAY 2: #10-19 all and 23-27 odds
Optional:Check out: Graphing program online: DesmosOrhttp://www.padowan.dk/