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Trigonometry
Objectives: The Student Will … Find trigonometric ratios using right
Triangles Solve problems using trigonometric
ratiosHOMEWORK: Sin, cos, tan Practice WS `
Trigonometric Ratios SOH CAH TOA
Opposite Sine =
Adjacent Cosine =
Tangent =
Hypotenuse
Hypotenuse
AdjacentOpposite
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)
OppSin L =
817
15
= = 0.4706Hyp
817
AdjCos L = = = 0.8825
Hyp1517
OppTan L = = = 0.5333Adj
815
Hypotenuse
N
M L
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)
OppSin N =
817
15
= = 0.8825Hyp
1517
AdjCos N = = = 0.4706
Hyp817
OppTan N = = = 1.875
Adj158
Hypotenuse
N
M L
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 =
b.) cos 89 =
Make sure your
calculator is in degree
mode
1.4826
0.0175
Example 3:Find x.
24°
19
x
1.)
31°
2.)
x
34
tan 24° = x19
(tan 24°)19 =x
8.459345021 = x
8.4593 ≈ x
cos 31° = x34
(cos 31°)34 =x
29.14368822 = x
29.1437 ≈ 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?
oppsin 7 =
5(sin 7) = (5)y5
5(sin 7) = y
Convert to inches y = 12(0.6093467)
Hypotenuse
Opposite
0.6093467 ft = y
y ≈ 7.3121 in
y5=
hyp
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,
b.) cos R = 0.6401,
ᵝ ≈ 13.3°
tan-1(0.2356) = ᵝ
cos-1(0.6401) = RR ≈ 50.2°
Example 6:Find x.
18 15
x°
tan x° =1518
x°
39.80557109° = x
39.81° ≈ x
tan-1 ( ) =1518
Example 7:Find x.
17 12
x°
sin x° =1217
(sin x°)17 =12
44.90087216° = x
(sin x°)17 =12
17 17
(sin x°) = 12
17
(sin-1 ) = x12
17
44.9° ≈
Study Guide pg 370Find x. Round to the nearest tenth.
Study Guide pg 370Find x. Round to the nearest tenth.