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 sine function with amplitude 2 (vertical stretch by factor 2, range [-2,2]) and period 360° (same as basic sine). Key points in \( 0^\circ \leq x \leq 360^\circ \):

• X-intercepts: Where \( \sin(x)=0 \), so \( x=0^\circ, 180^\circ, 360^\circ \) → points (0°,0), (180°,0), (360°,0).
• Maximum: \( \sin(x)=1 \) at \( x=90^\circ \) → \( y=2(1)=2 \) → (90°,2).
• Minimum: \( \sin(x)=-1 \) at \( x=270^\circ \) → \( y=2(-1)=-2 \) → (270°,-2).

To graph: Plot these key points, draw a smooth wave connecting them, label axes as "Angle (degrees)" (x-axis) and "y-value" (y-axis).

Answer:

Key points to plot: (0°, 0), (90°, 2), (180°, 0), (270°, -2), (360°, 0). The graph is a sine wave with amplitude 2, oscillating between -2 and 2 over 0° to 360°, labeled as specified.