Transparency 4. Transparency 4a Chapter 9 Right Triangles and Trigonometry Section 9.5 Sine, Cosine, Tangent.

Chapter 9Right Triangles and Trigonometry

Section 9.5

Sine, Cosine, Tangent

Definitions

A trigonometric ratio is the ratio of the side lengths of two sides of a right triangle

The three basic trigonometric ratios are Sine, Cosine, and tangent

C A

B

c hypotenuseSide opposite A

a

Side adjacent to A

b

sideoppsite ASin A

hypotenuse

sideadjacent ACos A

hypotenuse

sideoppsite ATan A

sideadjacent A

a

c

b

c

a

b

Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.

Answer:

Find sin A, cos A, tan A, sin B, cos B, and tan B. Express each ratio as a fraction.

Answer:

Use a calculator to find tan to the nearest ten thousandth.

KEYSTROKES: 56 1.482560969TAN ENTER

Answer:

KEYSTROKES: 90 0COS ENTER

Answer:

Use a calculator to find cos to the nearest ten thousandth.

a. Use a calculator to find sin 48° to the nearest ten thousandth.

b. Use a calculator to find cos 85° to the nearest ten thousandth.

Answer:

Answer:

EXERCISING A fitness trainer sets the incline on a treadmill to The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor?

Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches.

KEYSTROKES: 60 7 7.312160604SIN ENTER

Multiply each side by 60.

Use a calculator to find y.

Answer: The treadmill is about 7.3 inches high.

CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about how high does the ramp rise off the ground to the nearest inch?

Answer: about 15 in.

Find the value of each variable

sin3610

x

cos3610

y

x = 10sin 36y = 10cos 36

x 5.8779 y 8.090

sideoppsite ASin A

hypotenuse

sideadjacent ACos A

hypotenuse

Find the value of each variable

tan 488

x

8cos48

y

x = 8tan 48

y(cos 48) = 8

x 8.8849 y 11.9558

sideadjacent ACos A

hypotenuse

sideoppsite A

Tan Asideadjacent A

8

cos48y

Find the value of each variable

x = 8(cos 64)

x 3.5070

y = 8(sin 64)

x 7.1903