The trigonometric function that best models the data is determined as y = 1.87sin(–0.29x + 4.79) + 6.13.
<h3>Trigonometric function that models the data</h3>
The trigonometric function that best models the data is determined as follows;
y = 1.87sin(-0.29x + 4.79) + 6.13
Use the above equation to check if its gives you values in the table;
<h3>when x = 1</h3>
y = 1.87sin(-0.29 x 1 + 4.79) + 6.13
y = 1.87sin(4.5 rad) + 6.13
y = 4.3
<h3>when x = 2</h3>
y = 1.87sin(-0.29 x 2 + 4.79) + 6.13
y = 1.87sin(4.21 rad) + 6.13
y = 4.49
<h3>when x = 4</h3>
y = 1.87sin(-0.29 x 4 + 4.79) + 6.13
y = 1.87sin(3.63 rad) + 6.13
y = 5.2
<h3>when x = 7</h3>
y = 1.87sin(-0.29 x 7 + 4.79) + 6.13
y = 1.87sin(2.76 rad) + 6.13
y = 6.8
<h3>when x = 9</h3>
y = 1.87sin(-0.29 x 9 + 4.79) + 6.13
y = 1.87sin(2.18 rad) + 6.13
y =7.7
<h3>when x = 10</h3>
y = 1.87sin(-0.29 x 10 + 4.79) + 6.13
y = 1.87sin(1.89 rad) + 6.13
y = 7.9
<h3>when x = 13</h3>
y = 1.87sin(-0.29 x 13 + 4.79) + 6.13
y = 1.87sin(1.02 rad) + 6.13
y = 7.72
<h3>when x = 17</h3>
y = 1.87sin(-0.29 x 17 + 4.79) + 6.13
y = 1.87sin(-0.14 rad) + 6.13
y = 5.9
<h3>when x = 20</h3>
y = 1.87sin(-0.29 x 20 + 4.79) + 6.13
y = 1.87sin(-1.01 rad) + 6.13
y = 4.6
Thus, the trigonometric function that best models the data is determined as y = 1.87sin(–0.29x + 4.79) + 6.13.
Learn more about trigonometry functions here: brainly.com/question/1143565
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is the x component of the vertex, in your case, the vertex is the highest point