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Published byAdelia Hunt Modified over 9 years ago
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Graphing Trigonometric Functions Objective: To graph various trigonometric functions. VERTICAL DISPLACEMENT The graph of y = A sin(k + c) + h is the graph of y = A sin(k + c) translated h units vertically. If h > 0, the graph is moved up, and if h < 0 then the graph is moved down. This applies to all the trig functions.
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G RAPH Y = COS AND Y = COS -1 ON THE SAME SET OF AXES. E XPLAIN THE SIMILARITIES AND DIFFERENCES BETWEEN THE GRAPHS. 0°45°90°135°180°225°270°315°360° Cos 10.710-0.71-0.7100.711 Cos - 1 0-0.29-1.71-2-1.71-0.290
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G RAPH Y = 4 SIN 2 Find the amplitude, period and phase shift. Amplitude = |A| = 4Period = 360 2 = 180° Phase Shift = 0202 = 0
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G RAPH Y = TAN ( ) x - p 2 6 Period = ½½ = 2 Phase Shift = - 6. ½ = 33
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Compound functions may consist of sums or products of trigonometric functions. For example, y = sin x ∙ cos x is a compound function that contains a product of trig functions. Compound functions can also include sums or products of trig functions and other functions. For example, y = sin x + x is a compound function that is the sum of a trig function and a linear function. Compound Functions
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Graph y = sin x + x x 0 2 3 /222 5 /233 sin x 010010 sin x + x 02.573.143.716.288.859+.42 ● ● ● ● ● ● ●
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Graph y = x cos x x 0 /2 3 /222 5 /233 y = x 0 /2 3 /222 5 /233 y = cos x 10010 y = x cos x 00 -- 0 22 0 -3
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A SSIGNMENT Page 326 # 13 - 30
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