Download Section 7-5

Section 7-5
The Other Trigonometric
Functions
Six Trig. Functions
sine (sin θ)
cosecant (csc θ)
cosine (cos θ)
secant (sec θ)
tangent (tan θ)
cotangent (cot θ)
Trig Formulas
y
sin θ =
r
r
csc θ =
y
x
cos θ =
r
sec θ = r
y
tan θ =
x
x
cot θ =
y
x
Formulas in terms of sin and cos
tan θ = sin 
cos 
1
sec θ =
cos 
cos 
cot θ =
sin 
1
csc θ =
sin 
Positive Quadrants
Using a Calculator
Because we do not have secant, cosecant,
and cotangent buttons on the calculator, we
need to use the formulas of these functions
that are given in terms of sine, cosine, and
tangent.
Using a Calculator
Example 1: Use a calculator to find sec 22º.
1
sec  
cos 
1
sec 22 
cos 22
1
sec 22 
0.9272
sec 22  1.08
Using a Calculator
Example 2: Use the calculator to find cot 185º.
1
cot  
tan 
1
cot 185 
tan 185
1
cot 185 
0.0875
cot 185  11.430
Using a Calculator
Example 3: Use a calculator to find csc 3.
1
csc  
sin 
csc 3 
1
sin 3
1
csc 3 
0.1411
csc 3  7.09
Given a quadrant and one of the trig
functions of θ we can use the formulas and
the circle formula to find the other five trig
functions.
Finding Trig. Functions
Example 4:
Find the value of the other five trig. functions if
5
tan θ =
and π < θ < 2π.
12
*First, determine which quadrant the angle is in.*
Finding Trig. Functions
• (continued) The angle must be in the third
quadrant.
5
• And we know tan θ =
12
HOMEWORK (Day 1)
pg. 285; (class exercises) 5 – 7 all
pg. 285; (written exercises) 1, 2
pg. 285
5) III
6) IV
7) a. cos θ = -3/5
c. cot θ = -3/4
e. csc θ = 5/4
b. tan θ = -4/3
d. sec θ = -5/3
1) a. -5.671 b. -0.1051 c. -1.043
2) a. 1.019 b. -1.252 c. -0.1425
d. -1.855
d. 0.6466
Example 5: Find the exact value of each expression
or state that the value is undefined.
a) sin 120° = 3
2
b) csc 120° =
2 3
3
c) cos 120° =
1
2
d) sec 120° =  2
e) tan 120° =  3
f) cot 120° =
 3
3
Example 6:
Find the exact value of each expression or
state that the value is undefined.
a) csc 90°
=1
b) sec 90°
= undefined
c) tan 90°
= undefined
d) cot 90°
=0
Graphing y = tan θ
• Use a calculator to fill in the chart.
• If you get an error for an answer, write
“undefined” in the box.
tan 0° =
tan 45° =
tan -45° =
tan 90° =
tan -90° =
tan 180° =
tan -180° =
tan 270° =
tan -270° =
tan 360° =
tan -360° =
Graphing y = tan θ
• Draw the x and y axes
• Draw the asymptotes at the undefined
values
• Plot the points where tangent is defined
Graph of y = tan θ
HOMEWORK (Day 2)
pg. 285; 9
pg. 286; 13, 15, 24 – 28 even