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serious [3.7K]
3 years ago
12

Let f(x) = sin x; Sketch the graph of f^2

Mathematics
1 answer:
Aleks [24]3 years ago
5 0

Answer:  see graph

<u>Step-by-step explanation:</u>

Look at the Unit Circle to see the coordinates of the quadrangles.

Build a sine table for one period (0° - 360°).

<u>     x    </u>  <u>  y = sin(x)     </u>     <u>  y² = (sin(x))²  </u>   <u>  (x, y²)   </u>  

    0°       sin(0°) = 0          (0)² = 0              (0°, 0)

   90°     sin(90°) = 1          (1)² = 1               (90°, 1)

  180°     sin(180°) = 0        (0)² = 0            (180°, 0)

  270°     sin(270°) = -1       (-1)² = 1             (270°, 1)

  360°     sin(360°) = 0       (0)² = 0            (360°, 0)

Now plot the (x, y²) coordinates on your graph.

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Calculate the average rate of change of f(x) = 1 x - x2 - 2 for 3 ≤ x ≤ 6. A) -163 18 B) -18 163 C) 163 18 D) 18 163
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To solve this we are going to use the average rate of change formula: A(x)= \frac{f(b)-f(a)}{b-a}
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f(b) is the position function evaluated at b
a is the first point in the interval
b is the second point in the interval

We can infer for our problem that the first point is 3 and the second point is 6, so a=3 and b=6. Lets replace those values in our formula:
A(x)= \frac{f(b)-f(a)}{b-a}
A(x)= \frac{f(6)-f(3)}{6-3}
A(x)= \frac{6-6^2-2-(3-3^2-2)}{3}
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We can conclude that the average rate of change of the function f(x) = 1 x - x2 - 2 for <span>3 ≤ x ≤ 6 is -8</span>
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