Concept

The terminal side of angle  in standard position Find Sine and Cosine Given a Point on the Unit Circle The terminal side of angle  in standard position intersects the unit circle at . Find cos  and sin . , Example 1

The terminal side of angle  in standard position intersects the unit circle at Find cos  and sin . A. B. C. D. Example 1

Determine the period of the function. Identify the Period Determine the period of the function. The pattern repeats at and so on. Example 2

Determine the period of the function. A. B. C. D. Example 2

Use Trigonometric Functions A. CYCLING The pedals on a bicycle rotate as the bike is being ridden. The height of a bicycle pedal varies periodically as a function of the time, as shown in the figure. Notice that the pedal makes one complete rotation every two seconds. Make a table showing the height of a bicycle pedal at 3.0, 3.5, 4.0, 4.5, and 5.0 seconds. Example 3

Use Trigonometric Functions At 3.0 seconds the pedal is in the same location as 3.0 – 2.0 or 1 second, which is 4 inches high. At 3.5 seconds the pedal is 11 inches high. At 4.0 seconds the pedal is 18 inches high. At 4.5 seconds the pedal is 11 inches high. At 5.0 seconds, the pedal is at 4 inches high. Answer: Example 3

B. CYCLING Identify the period of the function. Use Trigonometric Functions B. CYCLING Identify the period of the function. The period is the time it takes to complete one rotation. Answer: So, the period is 2 seconds. Example 3

Use Trigonometric Functions C. CYCLING Graph the function. Let the horizontal axis represent the time t and the vertical axis represent the height h in inches that the pedal is from the ground. The maximum height of the pedal is 18 inches, and the minimum height is 4 inches. Because the period of the function is 2 seconds, the pattern of the graph repeats in intervals of 2 seconds, such as from 3.0 seconds to 5.0 seconds. Example 3

Use Trigonometric Functions Answer: Example 3

A. STUNT CYCLING The pedals on a trick oversized bicycle rotate as the bike is being ridden. The height of a bicycle pedal varies periodically as a function of the time, as shown in the figure. Notice that the pedal makes one complete rotation every 4.0 seconds. Choose the correct table showing the height of a bicycle pedal at 0.0, 1.0, 2.0, 3.0, and 4.0 seconds. Example 3

A. B. C. D. Example 3

B. Identify the period of the function. A. 1.0 second B. 2.0 seconds C. 4.0 seconds D. 8.0 seconds Example 3

A. maximum height = 20 in. and minumum height = 10 in. C. Choose the correct maximum height and minimum height of the graph of the function if the horizontal axis represents the time t and the vertical axis represents the height in inches that the pedal is from the ground. A. maximum height = 20 in. and minumum height = 10 in. B. maximum height = 40 in. and minumum height = 0 in. C. maximum height = 40 in. and minumum height = 30 in. D. maximum height = 30 in. and minumum height = 10 in. Example 3

A. Find the exact value of cos 690°. Evaluate Trigonometric Functions A. Find the exact value of cos 690°. cos 690° = cos(330° + 360°) = cos 330° Example 4

B. Find the exact value of Evaluate Trigonometric Functions B. Find the exact value of Example 4

A. Find the exact value of cos 660°. B. C. D. Example 4

B. Find the exact value of Example 4