Question

question: consider the function ( y = 2sin(x) ) for ( 0^circ leq x leq 360^circ ). 1. graph the function: plot the function ( y = 2sin(x) ) on a coordinate plane. label the x-axis as \angle (degrees)\ and the y-axis as \y-value\. mark the coordinates of all key points where the graph intersects the x-axis, reaches its maximum, or minimum within the given interval.

Explanation:

Step1: Identify key points

Key points are intersections with x-axis, maxima, minima. For \(y=2\sin(x)\):

• X-intercepts: \(x=0^\circ, 180^\circ, 360^\circ\) (since \(\sin(x)=0\) here), so coordinates \((0^\circ,0)\), \((180^\circ,0)\), \((360^\circ,0)\).
• Maxima: \(\sin(x)=1\) at \(x=90^\circ\), so \(y=2\), coordinate \((90^\circ,2)\).
• Minima: \(\sin(x)=-1\) at \(x=270^\circ\), so \(y=-2\), coordinate \((270^\circ,-2)\).

Step2: Plot the graph

Draw x-axis labeled "Angle (degrees)" (0° to 360°) and y-axis labeled "y-value" (-2 to 2). Plot the key points and connect them with a smooth sine wave.

Answer:

The graph of \(y=2\sin(x)\) for \(0^\circ\leq x\leq360^\circ\) has key points:

• X-intercepts: \((0^\circ,0)\), \((180^\circ,0)\), \((360^\circ,0)\)
• Maximum: \((90^\circ,2)\)
• Minimum: \((270^\circ,-2)\)

Plot these points and draw a smooth wave between them, oscillating between -2 and 2, crossing the x-axis at the listed angles.