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In this section, we used the product-to-sum formulas to write sums and differences of trigonometric functions. Another type of expression involving the sum or difference of sine and cosine terms is a Fourie series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form A, + (A, cos x + B, sin x) + (Az cos 2x + B, sin 2x) + (A, cos 3x + B, sin 3x) + .. where A,, A2, A3, . and B1, B2, B3, . are constants. Fourier proved that any continuous function can be represented by a Fourier series. In Exercises 49-50, we use Fourier polynomials (a finite number of terms from a Fourier se to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave 50. A "square" wave is a periodic wave that alternates between two fixed values with equal time spent at each value and with negligible transition time between them. Square waves have practical uses in electronics and music, and because of their rectangular pattern, they are used in timing devices to synchronize circuits. Given, )3D sin Tx + a. Graph the first three terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1]. b. Graph the first five terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1].

In this section, we used the product-to-sum formulas to write sums and differences of trigonometric functions. Another type of expression involving the sum or difference of sine and cosine terms is a Fourie series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form A, + (A, cos x + B, sin x) + (Az cos 2x + B, sin 2x) + (A, cos 3x + B, sin 3x) + .. where A,, A2, A3, . and B1, B2, B3, . are constants. Fourier proved that any continuous function can be represented by a Fourier series. In Exercises 49-50, we use Fourier polynomials (a finite number of terms from a Fourier se to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave 50. A "square" wave is a periodic wave that alternates between two fixed values with equal time spent at each value and with negligible transition time between them. Square waves have practical uses in electronics and music, and because of their rectangular pattern, they are used in timing devices to synchronize circuits. Given, )3D sin Tx + a. Graph the first three terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1]. b. Graph the first five terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1].

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 68E
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In this section, we used the product-to-sum formulas to write sums and differences of trigonometric functions. Another type of expression involving the sum or difference of sine and cosine terms is a Fourie series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form A, + (A, cos x + B, sin x) + (Az cos 2x + B, sin 2x) + (A, cos 3x + B, sin 3x) + .. where A,, A2, A3, . and B1, B2, B3, . are constants. Fourier proved that any continuous function can be represented by a Fourier series. In Exercises 49-50, we use Fourier polynomials (a finite number of terms from a Fourier se to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave
Transcribed Image Text:In this section, we used the product-to-sum formulas to write sums and differences of trigonometric functions. Another type of expression involving the sum or difference of sine and cosine terms is a Fourie series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form A, + (A, cos x + B, sin x) + (Az cos 2x + B, sin 2x) + (A, cos 3x + B, sin 3x) + .. where A,, A2, A3, . and B1, B2, B3, . are constants. Fourier proved that any continuous function can be represented by a Fourier series. In Exercises 49-50, we use Fourier polynomials (a finite number of terms from a Fourier se to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave
50. A "square" wave is a periodic wave that alternates between two fixed values with equal time spent at each value and with negligible transition time between them. Square waves have practical uses in electronics and music, and because of their rectangular pattern, they are used in timing devices to synchronize circuits. Given, )3D sin Tx + a. Graph the first three terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1]. b. Graph the first five terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1].
Transcribed Image Text:50. A "square" wave is a periodic wave that alternates between two fixed values with equal time spent at each value and with negligible transition time between them. Square waves have practical uses in electronics and music, and because of their rectangular pattern, they are used in timing devices to synchronize circuits. Given, )3D sin Tx + a. Graph the first three terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1]. b. Graph the first five terms of the Fourier series on the window [-4, 4, 1] by [-2, 2, 1].
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