Questions: (a) The sine and cosine curves y=a sin (k x) and y=a cos (k x), k>0 have amplitude and period. The sine curve y=5 sin (2 x) has amplitude, period π, an appropriate interval to graph one period is (0, ). (b) Graph one period of y=5 sin (2 x) and label the x-coordinates of the key points used for graphing the function.

(a) The sine and cosine curves y=a sin (k x) and y=a cos (k x), k>0 have amplitude and period. The sine curve y=5 sin (2 x) has amplitude, period π, an appropriate interval to graph one period is (0, ).

(b) Graph one period of y=5 sin (2 x) and label the x-coordinates of the key points used for graphing the function.
Transcript text: (a) The sine and cosine curves $y=a \sin (k x)$ and $y=a \cos (k x), k>0$ have amplitude $\square$ and period $\square$ - The sine curve $y=5 \sin (2 x)$ has amplitude $\square$ period $\pi$ an appropriate interval to graph one period is $(0$, $\square$ ). (b) Graph one period of $y=5 \sin (2 x)$ and label the $x$-coordinates of the key points used for graphing the function.
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Solution

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Solution Steps

Step 1: Identify the amplitude and period of the sine and cosine curves
  • The sine and cosine curves y=asin(kx) y = a \sin(kx) and y=acos(kx) y = a \cos(kx) have amplitude a a and period 2πk \frac{2\pi}{k} .
Step 2: Determine the amplitude and period of the given sine curve
  • The sine curve y=5sin(2x) y = 5 \sin(2x) has amplitude 5 5 and period 2π2=π \frac{2\pi}{2} = \pi .
Step 3: Identify the appropriate interval to graph one period
  • An appropriate interval to graph one period of y=5sin(2x) y = 5 \sin(2x) is [0,π] [0, \pi] .

Final Answer

  • Amplitude: 5 5
  • Period: π \pi
  • Appropriate interval: [0,π] [0, \pi]
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