Pg. 323/361 Homework
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Pg. 362
#39 – 47 odd, 51, 52
Memorize Trig. Info
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#2
#8
#12
#16
#20
#24
#30
#36
#42
#48
#1
#4
#7
#8
#11
QIV
#4
-250°
#10
338°, 698°, -382°, -742°
11π/4, -5π/2
π/4, 9π/4, -15π/4, -23π/4
78°, 168°
#26
90°, π/2
#32
-120°, -2π/3
#38
π/3
#44
59π/90
#50
8
#2
113
7/8
#5
7
113
11/15
2 26
11
,8
113
, 7 , 8 , 113 , 113
8 7
8
7
#9
#12
QIII
#6
QIII
470°
#14
210°, 570°, -510°, -870°
#18
29π/6, -19π/6
#22
67°, 157°
5π/12, 11π/12
#28
π/14, 4π/7
135°, 3π/4
#34
0°, 0, 2π
-600°, -10π/3
#40
-1260°, -7π
7π/6
#46
11π/6
249π/180
#52
810/π
7
#3
8/7
113
113
#6
113
8
7
2 26
15
15
2 26
#10
#13
11
2 26
15/11
6.5 Trig Functions of an Acute Angle
Trig Functions
• The six trig functions of any
angle 0° < Ɵ < 90° are
defined as follows:
opp
hyp
adj
cos  
hyp
opp
tan  
adj
sin  
adj
opp
hyp
sec  
adj
hyp
csc  
opp
cot  
• Also, we know that from the
basic three trig functions:
1
tan 
1
sec  
cos 
1
csc  
sin 
cot  
6.5 Trig Functions of an Acute Angle
Triangle Trig
• We use right triangles
because they allow us to
use the Pythagorean
Theorem, which makes
solving a much easier
process!
• Because 30°, 45° and 60°
occur frequently, we will
learn and memorize those
triangles!!
• If c = 2, determine the
lengths of a and b and find
the six trig values at 30° and
60°.
6.5 Trig Functions of an Acute Angle
More Trig Triangles
• If a = 1, determine the
length of c and find the six
trig values.
Cofunctions of Complementary
Angles
• If Ɵ is any acute trig angle, a
trig function value of Ɵ is
equal to the cofunction of
the complement of Ɵ, as
follows:




sin   cos     cot   tan    
2

2



cos   sin    
2



sec   csc    
2



tan   cot    
2



csc   sec    
2

6.5 Trig Functions of an Acute Angle
Example:

• Show that sin   cos    
2

are cofunctions.
• Let Ɵ be an acute angle
such that sin Ɵ = 5/6. Find
all the trig functions of Ɵ.
• One angle of a right triangle
measures 38°, and the
hypotenuse has length of
17. Find the measures of
the remaining sides.
6.5 Trig Functions of an Acute Angle
Example:
• They hypotenuse and one
leg of a triangle measure 12
and 7 respectively. Find the
measure of angle Ɵ formed
by these two sides.
Trig Functions of Any Angle
• Let Ɵ be an angle in
standard position, P(x, y) a
point other than the origin
on the terminal side of P,
and r = x 2  y 2
The six trig values of Ɵ are
defined as follows:
y
x
sin  
cos  
tan  
r
r
r
r
sec  
csc  
cot  
x
y
y
x
x
y
6.5 Trig Functions of an Acute Angle
Example:
• Find the values of the six
trig functions at an angle Ɵ
in standard form with point
P(4, 7) on its terminal side.
• **Note** If an angle does
not appear acute in the first
quadrant, you can work in
any of the four quadrants to
make the angle acute!!
• Find the values of all six trig
functions and the angle of
measure of angle Ɵ, where
P(-3, 2) is a point on the
terminal side of Ɵ.
• Find all the values of all six
trig functions for the
quadrantal angles of:

3
0, ,  ,
, 2
2
2