Question

question: consider the function ( y = 2sin(x) ) for ( 0^{circ}leq xleq360^{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:

The function \(y = 2\sin(x)\) is a vertical stretch of the basic sine function \(y = \sin(x)\) by a factor of 2. Key points in \(0^\circ \leq x \leq 360^\circ\) include:

• X-intercepts (where \(y=0\)): \((0^\circ, 0)\), \((180^\circ, 0)\), \((360^\circ, 0)\)
• Maximum point (since amplitude = 2): \((90^\circ, 2)\)
• Minimum point: \((270^\circ, -2)\)

Plot these points on a coordinate plane with x-axis labeled "Angle (degrees)" and y-axis labeled "y-value", then connect them smoothly to form the sine wave.

Answer:

Key points to plot: \((0^\circ, 0)\), \((90^\circ, 2)\), \((180^\circ, 0)\), \((270^\circ, -2)\), \((360^\circ, 0)\). The graph is a sine wave with amplitude 2 over \(0^\circ\) to \(360^\circ\).