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.