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Finney Chapter 1.6. Radian Measure Example 1: Finding Arc Length.

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Presentation on theme: "Finney Chapter 1.6. Radian Measure Example 1: Finding Arc Length."— Presentation transcript:

1 Finney Chapter 1.6

2 Radian Measure

3

4 Example 1: Finding Arc Length

5 Periodicity

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7

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10 Even & Odd Trigonometric Functions

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12 Standard Position of an Angle

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15 Example 3: Finding Trigonometric Values

16 Transformation of Trigonometric Graphs

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18 Example 4: Graphing a Trigonometric Function

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20 Example 5: Finding the Frequency of a Musical Note Consider the tuning fork data in Table 1.18 (Finney, page 49). (a)Find a sinusoidal regression equation (general sine curve) for the data and superimpose its graph on a scatter plot of the data (b)The frequency of a musical note, or wave, is measured in cycles per second, or hertz (1 Hz = 1 cycle per second). The frequency is the reciprocal of the period of the wave, which is measured in seconds per cycle. Estimate the frequency of the note produced by the tuning fork. NOTE: there are many data points, so rather than do this in class, I will simply reprint what is in your textbook

21 Example 5: Finding the Frequency of a Musical Note

22 Inverse Trigonometric Functions None of the trigonometric functions is one-to-one We can define inverse trigonometric functions by appropriately restricting their domains Recall that, for the inverse of a function, the domain and range switch roles Hence, in order to appropriately restrict the domains of the trigonometric functions, we must consider their range; an inverse function must cover the entire range (which becomes the domain)

23 Inverse Trigonometric Functions

24 DEFINITIONS: FunctionDomainRange

25 Example 7: Finding Angles in Degrees & Radians

26 Example 8: Using the Inverse Trigonometric Functions

27 Exercise 1.6 Finney page 52, #1-14, 17-22, 24, odds, 41-49


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