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Chapter 9 Right 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 hypotenuse Side opposite  A a Side adjacent to  A b

Example 4-1a Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.

Example 4-1b

Example 4-1c

Example 4-1d

Example 4-1e Answer:

Example 4-1f Find sin A, cos A, tan A, sin B, cos B, and tan B. Express each ratio as a fraction.

Example 4-1g Answer:

Example 4-2a Use a calculator to find tan to the nearest ten thousandth. KEYSTROKES: TANENTER Answer:

Example 4-2b KEYSTROKES: 90 0 COSENTER 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. Example 4-2c Answer:

Example 4-3a 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.

Example 4-3b KEYSTROKES: SINENTER Multiply each side by 60. Use a calculator to find y. Answer: The treadmill is about 7.3 inches high.

Example 4-3c 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.

Example 4-4a Find the value of each variable x = 10sin 36 y = 10cos 36 x  y  8.090

Example 4-5a Find the value of each variable x = 8tan 48 y(cos 48) = 8 x  y 

Example 4-5b Find the value of each variable x = 8(cos 64) x  y = 8(sin 64) x 