Solutions Modeling Dynamics of Life 3ed Adler - Chapter 1.8

1.8.3 Use the table or a calculator to find the values of sine and cosine for the following inputs (in radians), and plot them on
a. a graph of sin(θ),
b. a graph of cos(θ),
c. as the coordinates of a point on the circle. θ =π/9.
Get solution

1.8.3 Use the table or a calculator to find the values of sine and cosine for the following inputs (in radians), and plot them on
a. a graph of sin(θ),
b. a graph of cos(θ),
c. as the coordinates of a point on the circle. θ =π/9.
Get solution

1.8.3 Use the table or a calculator to find the values of sine and cosine for the following inputs (in radians), and plot them on
a. a graph of sin(θ),
b. a graph of cos(θ),
c. as the coordinates of a point on the circle. θ =π/9.
Get solution

1.8.4 Use the table or a calculator to find the values of sine and cosine for the following inputs (in radians), and plot them on
a. a graph of sin(θ),
b. a graph of cos(θ),
c. as the coordinates of a point on the circle. θ = 5.0.
Get solution

1.8.5 Use the table or a calculator to find the values of sine and cosine for the following inputs (in radians), and plot them on
a. a graph of sin(θ),
b. a graph of cos(θ),
c. as the coordinates of a point on the circle. θ =−2.0.
Get solution

1.8.6 Use the table or a calculator to find the values of sine and cosine for the following inputs (in radians), and plot them on
a. a graph of sin(θ),
b. a graph of cos(θ),
c. as the coordinates of a point on the circle. θ = 3.2.
Get solution

1.8.7 Convert the following angles from degrees to radians or vice versa. 30?
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1.8.8 Convert the following angles from degrees to radians or vice versa. 330?
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1.8.9 Convert the following angles from degrees to radians or vice versa. 1?
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1.8.10 Convert the following angles from degrees to radians or vice versa. −30?
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1.8.11 Convert the following angles from degrees to radians or vice versa. 2.0 rad
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1.8.13 Convert the following angles from degrees to radians or vice versa. −π/5 rad
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1.8.13 Convert the following angles from degrees to radians or vice versa. −π/5 rad
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1.8.14 Convert the following angles from degrees to radians or vice versa. 30 rad
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1.8.15 The other trigonometric functions (tangent, cotangent, secant, and cosecant) are defined in terms of sin and cos by ... Calculate the value of each of these functions at the following angles (all in radians). Plot the points on a graph of each function. π/2
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1.8.16 The other trigonometric functions (tangent, cotangent, secant, and cosecant) are defined in terms of sin and cos by ... Calculate the value of each of these functions at the following angles (all in radians). Plot the points on a graph of each function. 3π/4
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1.8.17 The other trigonometric functions (tangent, cotangent, secant, and cosecant) are defined in terms of sin and cos by ... Calculate the value of each of these functions at the following angles (all in radians). Plot the points on a graph of each function. π/9
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1.8.18 The other trigonometric functions (tangent, cotangent, secant, and cosecant) are defined in terms of sin and cos by ... Calculate the value of each of these functions at the following angles (all in radians). Plot the points on a graph of each function. 5.0.
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1.8.19 The other trigonometric functions (tangent, cotangent, secant, and cosecant) are defined in terms of sin and cos by ... Calculate the value of each of these functions at the following angles (all in radians). Plot the points on a graph of each function. −2.0
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1.8.20 The other trigonometric functions (tangent, cotangent, secant, and cosecant) are defined in terms of sin and cos by ... Calculate the value of each of these functions at the following angles (all in radians). Plot the points on a graph of each function. 3.2
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1.8.21 The following are some of the most important trigonometric identities. Check them at
a. θ = 0,
b. θ = π/4,
c. θ = π/2,
d. θ =π. ... Only check at points a, c, and d.
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1.8.22 The following are some of the most important trigonometric identities. Check them at
a. θ = 0,
b. θ = π/4,
c. θ = π/2,
d. θ =π. ...
Get solution

1.8.23 The following are some of the most important trigonometric identities. Check them at
a. θ = 0,
b. θ = π/4,
c. θ = π/2,
d. θ =π. cos(θ − π)=−cos(θ).
Get solution

1.8.24 The following are some of the most important trigonometric identities. Check them at
a. θ = 0,
b. θ = π/4,
c. θ = π/2,
d. θ =π. ...
Get solution

1.8.25 The following are some of the most important trigonometric identities. Check them at
a. θ = 0,
b. θ = π/4,
c. θ = π/2,
d. θ =π. ...
Get solution

1.8.26 The following are some of the most important trigonometric identities. Check them at
a. θ = 0,
b. θ = π/4,
c. θ = π/2,
d. θ =π. sin(2θ)= 2 sin(θ) cos(θ).
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1.8.27 Convert the following sinusoidal oscillations to the standard form and sketch a graph. r ( t ) = 5.0[2.0 + 1.0 cos(2πt)].
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1.8.28 Convert the following sinusoidal oscillations to the standard form and sketch a graph. g ( t ) = 2.0 + 1.0 sin(t). (Hint: Use Exercise 24.) Exercise 24 ...
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1.8.29 Convert the following sinusoidal oscillations to the standard form and sketch a graph. f ( t ) = 2.0 − 1.0 cos(t). (Hint: Use Exercise 23.) Exercise 23 cos(θ − π)=−cos(θ).
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1.8.30 Convert the following sinusoidal oscillations to the standard form and sketch a graph. h ( t ) = 2.0 + 1.0 cos(2πt − 3.0).
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1.8.32 Find the average, minimum, maximum, amplitude, period, and phase from the graphs of the following oscillations ...
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1.8.32 Find the average, minimum, maximum, amplitude, period, and phase from the graphs of the following oscillations ...
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1.8.34 Find the average, minimum, maximum, amplitude, period, and phase from the graphs of the following oscillations ...
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1.8.34 Find the average, minimum, maximum, amplitude, period, and phase from the graphs of the following oscillations ...
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1.8.35 Graph the following functions. Give the average, maximum, minimum, amplitude, period, and phase of each and mark them on your graph. ...
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1.8.36 Graph the following functions. Give the average, maximum, minimum, amplitude, period, and phase of each and mark them on your graph. g ( t ) = 4.0 + 3.0 cos[2π(t − 5.0)].
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1.8.37 Graph the following functions. Give the average, maximum, minimum, amplitude, period, and phase of each and mark them on your graph. ...
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1.8.38 Graph the following functions. Give the average, maximum, minimum, amplitude, period, and phase of each and mark them on your graph. ...
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1.8.39 Oscillations are often combined with growth or decay. Plot graphs of the following functions, and describe in words what you see. Make up a biological process that might have produced the result. f ( t )=1 + t + cos(2πt) for 0<t <4.
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1.8.40 Oscillations are often combined with growth or decay. Plot graphs of the following functions, and describe in words what you see. Make up a biological process that might have produced the result. h ( t )=t + 0.2 sin(2πt) for 0<t <4.
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1.8.41 Oscillations are often combined with growth or decay. Plot graphs of the following functions, and describe in words what you see. Make up a biological process that might have produced the result. ...
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1.8.42 Oscillations are often combined with growth or decay. Plot graphs of the following functions, and describe in words what you see. Make up a biological process that might have produced the result. ...
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1.8.43 Oscillations are often combined with growth or decay. Plot graphs of the following functions, and describe in words what you see. Make up a biological process that might have produced the result. ...
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1.8.44 Oscillations are often combined with growth or decay. Plot graphs of the following functions, and describe in words what you see. Make up a biological process that might have produced the result. ...
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1.8.45 Sleepiness has two cycles, a circadian rhythm with a period of approximately 24 hours and an ultradian rhythm with a period of approximately 4 hours. Both have phase 0 (starting at midnight) and average 0, but the amplitude of the circadian rhythm is 1.0 sleepiness unit and the ultradian is 0.4 sleepiness unit. Find the formula and sketch the graph of sleepiness over the course of a day due to the circadian rhythm.
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1.8.46 Sleepiness has two cycles, a circadian rhythm with a period of approximately 24 hours and an ultradian rhythm with a period of approximately 4 hours. Both have phase 0 (starting at midnight) and average 0, but the amplitude of the circadian rhythm is 1.0 sleepiness unit and the ultradian is 0.4 sleepiness unit. Find the formula and sketch the graph of sleepiness over the course of a day due to the ultradian rhythm.
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1.8.47 Sleepiness has two cycles, a circadian rhythm with a period of approximately 24 hours and an ultradian rhythm with a period of approximately 4 hours. Both have phase 0 (starting at midnight) and average 0, but the amplitude of the circadian rhythm is 1.0 sleepiness unit and the ultradian is 0.4 sleepiness unit. Sketch the graph of the two cycles combined.
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1.8.48 Sleepiness has two cycles, a circadian rhythm with a period of approximately 24 hours and an ultradian rhythm with a period of approximately 4 hours. Both have phase 0 (starting at midnight) and average 0, but the amplitude of the circadian rhythm is 1.0 sleepiness unit and the ultradian is 0.4 sleepiness unit. At what time of day are you sleepiest? At what time of day are you least sleepy?
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1.8.49 Consider the following functions. ...
a. Plot them all on one graph.
b. Plot the sum ...
c. Plot the sum ...
d. Plot the sum ...
e. What does this sum look like?
f. Try to guess the pattern, and add on ... This is an example of a Fourier series, a sum of cosine functions that add up to a square wave that jumps between values of −1 and 1.
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1.8.50 Use a computer to cobweb and graph solutions of the following discrete-time dynamical systems. Try three different initial conditions for each. Can you make any sense of what happens? Why don’t the solutions follow a sinusoidal oscillation? ...
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1.8.51 Plot the function f (x)=cos(2π · 440x) + cos(2π · 441x). Describe the result. If these were sounds, what might you hear? (This corresponds to playing two notes with the same amplitude and slightly different frequencies.)
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1.8.51 Plot the function f (x)=cos(2π · 440x) + cos(2π · 441x). Describe the result. If these were sounds, what might you hear? (This corresponds to playing two notes with the same amplitude and slightly different frequencies.)
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