College Algebra & Trigonometry, 2018a

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9.2. GRAPHING TRIGONOMETRIC FUNCTIONS 407 Lastly, we notice that this graph starts with a y-value of 0, then goes to the maximum, back through 0 to the minimum and then back to zero to form one complete wave. This is the signature of a sine function, so the answer to this problem would be: y =3sin2x Example 4 Deterimine an equation that satisfies the given graph. 5 0 9π 16 9π 8 27π 16 9π 4 −5 First note that the maximum y-value for the graph is 5 and the minimum is −5. This means that the amplitude is 5. Next we see that there is one complete period of the function between 0 and 9π 4 , this means that the period is 9π 4 . From this information, we know that A =5and that the period for the graph is 9π 4 . Since P = 2π 2π B , and B =2π P , then B = ( 9π )=2π∗ 4 9π =8 9 . 4
408 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS Lastly, this graph starts with a y-value of 5, which is the maximum y-value. It then goes to 0 and down to the minimum, back through 0 and then back to the maximum to form one complete wave. Since this is the signature of the cosine function, the answer to this problem would be: y =5cos 8 9 x
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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288 CHAPTER 6. SEQUENCES AND SERIES
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College Algebra & Trigonometry, 2018a

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