question:\nconsider the function ( y = 2sin(x) ) for ( 0^{circ}leq xleq360^{circ} ).\n1. graph the…

question:\nconsider the function ( y = 2sin(x) ) for ( 0^{circ}leq xleq360^{circ} ).\n1. graph the function:\nplot 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.

question:\nconsider the function ( y = 2sin(x) ) for ( 0^{circ}leq xleq360^{circ} ).\n1. graph the function:\nplot 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.

Answer

Explanation:

Step1: Find the x - axis intersection points

Set (y = 0), then (2\sin(x)=0), (\sin(x)=0). For (0^{\circ}\leq x\leq360^{\circ}), (x = 0^{\circ},180^{\circ},360^{\circ}).

Step2: Find the maximum and minimum points

The general form of a sine function is (y = A\sin(x)+k). Here (A = 2,k = 0). The maximum value of (\sin(x)) is (1) and the minimum value is (- 1). When (\sin(x)=1), (x = 90^{\circ}), (y=2\times1 = 2). When (\sin(x)=-1), (x = 270^{\circ}), (y=2\times(-1)=-2).

Answer:

  • Intersection points with the x - axis: ((0^{\circ},0),(180^{\circ},0),(360^{\circ},0))
  • Maximum point: ((90^{\circ},2))
  • Minimum point: ((270^{\circ},-2))