Download Trigonometric Ratios

Mr. Owh
Today is: Friday, April 7th, 2006
Lesson 9.5A – Trigonometric Ratios
• 75A, 75B, 75C, 75D, 76
Announcements:
• Chapter 9 is about Right Triangles & Trigonometry
• Chapter 9 Test is April 21.
• Extra Credit assignment.
1
Lesson 9.5A – Trigonometric Ratios
• Today’s Objectives:
Find the sine, the cosine, and the tangent of an
acute angle.
• Today’s Key Terms:
sine, cosine, tangent
• Materials Needed Today:
notebook, geometer/ruler, calculator
• Today’s Geometry Standards: 18, 19
2
Trigonometry
• Trigonometry:
Greek for “triangle measuring”
• Trigonometry is the study of special
relationships between angle measures
and side lengths of right triangles.
• The ratios are:
SINE, COSINE, and TANGENT
3
NC 75A: SINE
For right triangles the sine of an angle is
defined below:
B
c
A
a
b
Memorize It:
SOH
C
length of leg opposite A
sine of A 
length of hypotenuse
4
NC 75B: COSINE
For right triangles the cosine of an angle is
defined below:
B
c
A
a
b
Memorize It:
CAH
C
length of leg adjacent to A
cosine of A 
length of hypotenuse
5
NC 75C: TANGENT
For right triangles the tangent of an angle is
defined below:
B
c
A
a
b
Memorize It:
TOA
C
length of leg opposite A
tangent of A 
length of leg adjacent to A
6
B
NC 75D:
Trigonometric Ratios:
opposite
o
sin A 

hypotenuse h
adjacent
a
cos A 

hypotenuse h
opposite o
tan A 

adjacent a
c
A
a
b
C
Memorize It:
SOH-CAH-TOA
(so-ca-toe)
7
Example 1:
Express each trigonometric ratio as a fraction and
as a decimal (hundredths place):
J
5
K
Mr. Owh’s Tip:
13
12
L
Use J and L
&
use SOH-CAH-TOA
Answer:
sin J =
cos J =
tan J =
sin L =
cos L =
tan L =
8
Example 1:
Express each trigonometric ratio as a fraction and
as a decimal (hundredths place):
J
5
K
Mr. Owh’s Tip:
13
12
L
Use J and L
&
use SOH-CAH-TOA
Answer:
sin J = 12/13
cos J = 5/13
tan J = 12/5
sin L = 5/13
cos L = 12/13
tan L = 5/12
9
Example 2:
Set up the following ratios then solve for x and y.
N
x
P
Memorize It:
SOH
38
y
27
M
Answer: use sine
sin 27 = x / 38
38 sin 27 = x
38 (0.4539) = x
17.252  x
10
Example 2:
Set up the following ratios then solve for x and y.
N
x
P
Memorize It:
CAH
38
y
27
M
Answer: use cosine
cos 27 = y / 38
38 cos 27 = y
38 (0.8910) = y
33.858  y
11
Example 2:
Set up the following ratios then solve for x and y.
N
x
P
Memorize It:
TOA
38
y
27
M
Answer: use tangent
tan 27  x / y
12
Example 3:
Set up the cosine, sine, and tangent ratios of the
given angle, then solve for x and y.
x
Answer:
42
y
15
Memorize It:
SOH-CAH-TOA
(so-ca-toe)
cos 42 = x / 15
15 cos 42 = x
x  11.147
sin 42 = y / 15
15 sin 42 = y
y  10.037
tan 42 = y / x
13
HW G2 #16 (Due Tue 4/18)
Page 562
{3–15, 17–27 odd, 28–38, 48–51, 53, 54}
Copy Problems & Figures !!!
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