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