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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 Fourier series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form Ao + (A, cos x + B, sin x) + (A2 cos 2x + B2 sin 2x) + (A3 cos 3x + B3 sin 3x) + .. where A, A2, A3, . and B1, B,, Ba, . 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 series) to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave 49. A "saw-tooth" wave is a periodic wave that rises linearly upward and then drops sharply. In music, such waves are generated in digital synthesizers to give high-quality sound without distortion. Given, Page 607 1/ sin X sin 27x sin 3 Tx f(x) = a. Graph the first three terms of the function on the window [-4, 4, 11 by [-1, 1.5, 0.5]. b. Graph the first five terms of the function on the window [-4, 4, 1] by (-1, 1.5, 0.5].

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 Fourier series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form Ao + (A, cos x + B, sin x) + (A2 cos 2x + B2 sin 2x) + (A3 cos 3x + B3 sin 3x) + .. where A, A2, A3, . and B1, B,, Ba, . 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 series) to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave 49. A "saw-tooth" wave is a periodic wave that rises linearly upward and then drops sharply. In music, such waves are generated in digital synthesizers to give high-quality sound without distortion. Given, Page 607 1/ sin X sin 27x sin 3 Tx f(x) = a. Graph the first three terms of the function on the window [-4, 4, 11 by [-1, 1.5, 0.5]. b. Graph the first five terms of the function on the window [-4, 4, 1] by (-1, 1.5, 0.5].

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 65E
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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 Fourier series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form Ao + (A, cos x + B, sin x) + (A2 cos 2x + B2 sin 2x) + (A3 cos 3x + B3 sin 3x) + .. where A, A2, A3, . and B1, B,, Ba, . 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 series) to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave 49. A "saw-tooth" wave is a periodic wave that rises linearly upward and then drops sharply. In music, such waves are generated in digital synthesizers to give high-quality sound without distortion. Given, Page 607 1/ sin X sin 27x sin 3 Tx f(x) = a. Graph the first three terms of the function on the window [-4, 4, 11 by [-1, 1.5, 0.5]. b. Graph the first five terms of the function on the window [-4, 4, 1] by (-1, 1.5, 0.5].
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 Fourier series, named after Jean-Baptiste Joseph Fourier (1768-1830). A Fourier series is an expression of the form Ao + (A, cos x + B, sin x) + (A2 cos 2x + B2 sin 2x) + (A3 cos 3x + B3 sin 3x) + .. where A, A2, A3, . and B1, B,, Ba, . 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 series) to model a "saw-tooth" wave and a "square" wave. Saw-tooth wave Square wave 49. A "saw-tooth" wave is a periodic wave that rises linearly upward and then drops sharply. In music, such waves are generated in digital synthesizers to give high-quality sound without distortion. Given, Page 607 1/ sin X sin 27x sin 3 Tx f(x) = a. Graph the first three terms of the function on the window [-4, 4, 11 by [-1, 1.5, 0.5]. b. Graph the first five terms of the function on the window [-4, 4, 1] by (-1, 1.5, 0.5].
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