ch.8 The Trigonometric Functions

# ch.8 The Trigonometric Functions - Chapter 8 The...

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Unformatted text preview: Chapter 8 The Trigonometric Functions 8.2 Sinusoidal Functions and Their Graphs Key Points • Graphing y = Asin(B(t − h)) + k and • y = Acos(B(t − h)) + k • Amplitude, period, frequency and horizontal shift • Finding formulas for periodic functions using sine and cosine t 0.05 0.35 y Amplitude and Midline Example 1 State the midline and amplitude of the following sinusoidal functions: (a) y = 3 sin t + 5 (b) y = (4 − 3 cos t )/20. Solution Functions Modeling Change: A Preparation for Calculus, 4th t 2 8 y Midline y = 5 Midline y = 0.2 Graph of y = 3 sin t + 5 Graph of y = 0.2 − 0.15 cos t Amplitude = 3 Amplitude = 0.15 Amplitude and Midline The functions y = A sin t + k and y = A cos t + k have amplitude | A | and the midline is the horizontal line y = k . Functions Modeling Change: A Preparation for Calculus, 4th y x π- π 2 π Period of a Function sin x y = π period: 2 The period of a function is the x interval needed for the function to complete one cycle. The period of y = A sin bx is b π 2 The period of y = A cos bx is also b π 2 y x π- π 2 π π 3 π 4 cos x y = π period: 2 2 1 cos x y = π period: 4 sin 2 : y x period π = Period The functions y = sin( Bt ) and y = cos( Bt ) have period P = 2π/|B|. Functions Modeling Change: A Preparation for Calculus, 4th Finding Formulas for Functions Example 3 Find possible formulas for the functions f and g in the graphs Functions Modeling Change: A Preparation for Calculus, 4th 20 40 60 t 1 1 y This function has period 4π This function has period 20 y = f ( t ) y = g ( t ) Horizontal Shift The graphs of y = sin( B ( t − h )) and y = cos( B ( t − h )) are the graphs of y = sin( Bt ) and...
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ch.8 The Trigonometric Functions - Chapter 8 The...

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