(1) Trigonometry 6

(1) Trigonometry 6 - Pre Calculus Math 40S Explained...

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Pre – Calculus Math 40S: Explained! www.math40s.com 58 Trigonometry Lesson 6 Part I Graphing ABCD Now that we have looked at all the transformations separately, we can combine them together. y = a sin b ( θ ± c ) ± d When drawing a graph from an equation, we must pay close attention to the order. First we apply the stretches (a & b, in either order), then the translations (c & d, in either order). Example 1: Graph π θ 1 y = 2cos ( - )+3 2 4 Finally, do the vertical translation π θ 1 y = 2cos ( - )+3 2 4 First graph y = cos θ 4 π 3 π 2 π −π π 2 π 3 π 4 π 5 π -3 -2 -1 1 2 3 4 π 3 π 2 π −π π 2 π 3 π 4 π 5 π -3 -2 -1 1 2 3 4 π 3 π 2 π −π π 2 π 3 π 4 π 5 π -2 2 4 6 Next graph θ 1 y = 2cos 2 Now do the phase shift and move the graph one unit right. π θ 1 y = 2cos ( - ) 2 4 4 π 3 π 2 π −π π 2 π 3 π 4 π 5 π -3 -2 -1 1 2 3 Now graph θ 1 y = cos 2 4 π 3 π 2 π −π π 2 π 3 π 4 π 5 π -3 -2 -1 1 2 3
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Pre – Calculus Math 40S: Explained!
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