Trigonometry

Objectives: The Student Will …
Find trigonometric ratios using right Triangles
 Solve problems using trigonometric ratios
HOMEWORK: Sin, cos, tan Practice WS
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Trigonometric Ratios

SOH CAH TOA
Opposite
=
Hypotenuse

Sine

Cosine =
Adjacent
Hypotenuse

Tangent =
Opposite
Adjacent
Standard decimal  side lengths  ten thousandths (4)
 angle measures  hundredths (2)
Example 1:
Find sin L, cos L, tan L, sin N, cos N, and tan N.
Express each ratio as a fraction and as a decimal.
(ten-thousandths)
N
17
8
M
Opp
8
Sin L =
=
= 0.4706
Hyp 17
15
L
Adj
15
Cos L =
=
= 0.8825
Hyp 17
Opp
8
Tan L =
=
= 0.5333
Adj
15
Example 1: continued
Now lets do sin N, cos N, and tan N. Express
each ratio as a fraction and as a decimal.
(ten-thousandths)
Opp 15
Sin N =
=
= 0.8825
Hyp 17
N
17
8
M
15
L
Adj
8
Cos N =
=
= 0.4706
Hyp 17
Opp 15
Tan N =
=
= 1.875
Adj
8
Find the indicated trigonometric ratio as a fraction
and as a decimal.
If necessary, round to the nearest ten-thousandths.
1.) sin A
2.) tan B
3.) cos A
4.) cos B
5.) sin D
6.) tan E
7.) cos E
8.) cos D
Example 2:
Find each value to the nearest ten
thousandths.
a.) tan 56 = 1.4826
b.) cos 89 = 0.0175
Make sure
your
calculator is
in degree
mode
Example 3: Find x.
x
tan 24° =
19
1.)
x
24°
(tan 24°)19 =x
8.459345021 = x
8.4593 ≈ x
19
x
cos 31° =
34
(cos 31°)34 =x
2.)
34
29.14368822 = x
29.1437 ≈ x
31°
x
Example 4:
A fitness trainer sets the incline on a treadmill to 7.
The walking surface is 5 feet long. Approximately
how many inches did the trainer raise the end of
the treadmill from the floor?
y
sin 7 = opp =
5
hyp
y
5(sin 7) = (5)
5
5(sin 7) = y
0.6093467 ft = y
Convert to inches y = 12(0.6093467)
y ≈ 7.3121 in
Using Trigonometry to Find
the Angle Measure
We can also find an angle measure.
(hundredths place)
If sin θ = 0.7823, then sin-1(0.7823) = θ
This is done in the calculator:
Press the 2nd key, press the sin (sin-1) key
Type in 0.7823 and press enter
θ = 51.47
Examples 5:
Find the measure of each acute angle to the nearest
tenth degree.
a.) tan
ᵝ
= 0.2356, tan-1(0.2356) =
ᵝ ≈ 13.3°
ᵝ
cos-1(0.6401) = R
b.) cos R = 0.6401,
R ≈ 50.2°
Example 6: Find x.
tan x° =
tan-1
18
x°
15
15
18
15
(
) = x°
18
39.80557109° = x
39.81° ≈ x
Example 7: Find x.
sin x° =
12
17
(sin x°)17 = 12
17
x°
(sin x°)17 = 12
12
17
17
(sin x°) = 12
17
(sin-1
12
17
)=x
44.9° ≈ 44.90087216° = x
Study Guide pg 370
Find x. Round to the nearest tenth.
Study Guide pg 370
Find x. Round to the nearest tenth.