8-2
8-2 Trigonometric
TrigonometricRatios
Ratios
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
8-2 Trigonometric Ratios
<C
a
b
<B
c
b
Holt Geometry
8-2 Trigonometric Ratios
7)
Holt Geometry
x = 7.25
8-2 Trigonometric Ratios
Objectives
Find the sine, cosine, and tangent of an
acute angle.
Use trigonometric ratios to find side
lengths in right triangles and to solve
real-world problems.
Holt Geometry
8-2 Trigonometric Ratios
SOH-CAHopposite
sin x = hypotenus
TOA
e
opposite
tan x =
adjacent
adjacent
cos x =
hypotenus
e
Holt Geometry
8-2 Trigonometric Ratios
opposite
Sin(x)=hypotenus
e
ALWAYS an ANGLE!!!
Holt Geometry
8-2 Trigonometric Ratios
Writing Math
In trigonometry, the letter of the vertex of the
angle is often used to represent the measure of
that angle. For example, the sine of A is written
as sin A.
Holt Geometry
8-2 Trigonometric Ratios
Example 1: Finding Trigonometric Ratios
Write the trigonometric
ratio as a fraction and
as a decimal rounded to
the nearest hundredth.
sin J
60
sin J = 61
Holt Geometry
8-2 Trigonometric Ratios
Example 2: Finding Trigonometric Ratios
Write the trigonometric
ratio as a fraction and
as a decimal rounded to
the nearest hundredth.
cos J
11
cos J =61
Holt Geometry
8-2 Trigonometric Ratios
Example 3: Finding Trigonometric Ratios
Write the trigonometric
ratio as a fraction and
as a decimal rounded to
the nearest hundredth.
tan K
11
tan k =
60
Holt Geometry
8-2 Trigonometric Ratios
Example 4
Write the trigonometric
ratio as a fraction and as
a decimal rounded to
the nearest hundredth.
cos A
24
cos A =25
Holt Geometry
8-2 Trigonometric Ratios
Example 5:
Write cos 30° as a fraction.
Holt Geometry
s√3 = √3
cos 30 2s
2
=
√3
cos 30 2
=
8-2 Trigonometric Ratios
Example 6
Use a special right triangle to write tan 45°
as a fraction.
Draw and label a 45º-45º-90º ∆.
45°
s
45°
s
tan 45 = s =1
s
Holt Geometry
8-2 Trigonometric Ratios
Example 7
Use your calculator to find the trigonometric
ratio. Round to the nearest hundredth.
sin 52°
Caution!
Be sure your
calculator is in
degree mode, not
radian mode.
sin 52°  0.79
Holt Geometry
8-2 Trigonometric Ratios
Example 8
Use your calculator to find the trigonometric
ratio. Round to the nearest hundredth.
cos 19°
cos 19°  0.95
Holt Geometry
8-2 Trigonometric Ratios
hyp
EXAMPLE 9
opp
x
adj
The trigonometric functions are:
sine, cosine, tangent, cotangent, secant, and cosecant.
opp
adj tan x =
sin x =
cos x =
hyp
hyp
hyp
hyp
csc x = opp
sec x =
cot x =
adj
S OH C AH T OA
Holt Geometry
opp
adj
adj
opp
8-2 Trigonometric Ratios
13
EXAMPLE 10
5
x
12
Find the following:
sine, cosine, tangent, cotangent, secant, and cosecant.
12
sin x = 5
cos x =
tan x =
13
13
13
13
csc x =
sec x =
cot x =
5
12
S OH C AH T OA
Holt Geometry
5
12
12
5
8-2 Trigonometric Ratios
EXAMPLE 11
5
4
Find the following:
sine, cosine, tangent, cotangent, secant, and cosecant.
3
sin x = 4
cos x =
tan x =
5
5
5
5
csc x = 4
sec x =
cot x =
3
S OH C AH T OA
Holt Geometry
x
3
4
3
3
4
8-2 Trigonometric Ratios
EXAMPLE 12
Opposite
Adjacent
sin x =
csc x = 5
3
Holt Geometry
3
5
So… the
hypotenuse = 5
cos x =
4
5
tan x =
3
4
sec x =
5
4
cot x =
4
3
8-2 Trigonometric Ratios
Caution!
Do not round until the final step of your answer.
Use the values of the trigonometric ratios
provided by your calculator.
Holt Geometry
8-2 Trigonometric Ratios
Example 13
Find the length. Round to
the nearest hundredth.
opp
BC
BC  38.07 ft
Holt Geometry
adj
8-2 Trigonometric Ratios
Example 14:
Find the length. Round to
the nearest hundredth.
opp
QR
hyp
12.9(sin 63°) = QR
11.49 cm  QR
Holt Geometry
8-2 Trigonometric Ratios
Example 15
Find the length. Round to the
nearest hundredth.
FD
hyp
adj
FD  25.74 m
Holt Geometry