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Warm up

Warm up. Determine the angular displacement in radians of 471 revolutions. Round to the nearest hundredth. Determine the angular displacement in radians of 9.3 revolutions. Round to the nearest hundredth.

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Warm up

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  1. Warm up • Determine the angular displacement in radians of 471 revolutions. Round to the nearest hundredth. • Determine the angular displacement in radians of 9.3 revolutions. Round to the nearest hundredth. • Determine the angular velocity if 450 revolutions are completed in 12 minutes. Round to the nearest hundredth. • Determine the angular velocity if 7.6 revolutions are completed in 11 seconds. Round to the nearest hundredth. • Determine the linear velocity of a point rotating at an angular velocity of 75 radians per second at a distance of 40 inches from the center of the rotating object. Round to the nearest tenth. 2959.4 radians 58.4 radians 235.6 radians/min 4.3 rad/s 3000 in/s

  2. Vocabulary: Periodic Period 6-3 Graphing Sine and Cosine Functions

  3. METEOROLOGY The average monthly temperatures for a city demonstrate a repetitious behavior. For cities in the Northern Hemisphere, the average monthly temperatures are usually lowest in January and highest in July. The graph below shows the average monthly temperatures (°F) for Baltimore, Maryland, and Asheville, North Carolina, with January represented by 1.

  4. Example 5 Month 13 is January of the second year. To find the average temperature of this month, substitute this value into each equation. • What is the average temperature for each city in month 13?

  5. Homework • P363 #19-35 Odd, 51-53A, 55

  6. 6-4 Amplitude and Period of Sine and Cosine Functions • Recall from Chapter 3 that changes to the equation of the parent graph can affect the appearance of the graph by dilating, reflecting, and/or translating the original graph. In this lesson, we will observe the vertical and horizontal expanding and compressing of the parent graphs of the sine and cosine functions. • Let’s consider an equation of the form y=AsinӨ. We know that the maximum absolute value of sinӨis 1. Therefore, for every value of the product of sinӨand A, the maximum value of AsinӨis Similarly, the maximum value of AcosӨis . The absolute value of A is called the amplitude of the functions y=AsinӨand y=AcosӨ.

  7. Exit Ticket

  8. Homework • P373 #17-25 Odd, 37-47 Odd, 57-60A • Mid Chapter Quiz on P377

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