question:\nconsider the function ( y = 2 sin ( x ) ) for ( 0 ^ { circ } leq x leq 360 ^ { circ } ).\n1…

question:\nconsider the function ( y = 2 sin ( x ) ) for ( 0 ^ { circ } leq x leq 360 ^ { circ } ).\n1. graph the function:\nplot the function ( y = 2 sin ( 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 = 2 sin ( x ) ) for ( 0 ^ { circ } leq x leq 360 ^ { circ } ).\n1. graph the function:\nplot the function ( y = 2 sin ( 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: Determine the amplitude

The general form of a sine function is (y = A\sin(x)), where (A) is the amplitude. For (y = 2\sin(x)), (A = 2). This means the maximum value of (y) is (2) and the minimum value is (- 2).

Step2: Find the x - intercepts

Set (y=0), so (2\sin(x)=0). Then (\sin(x) = 0). For (0^{\circ}\leq x\leq360^{\circ}), (x = 0^{\circ},180^{\circ},360^{\circ}). The coordinates of the x - intercepts are ((0^{\circ},0)), ((180^{\circ},0)), ((360^{\circ},0))

Step3: Find the maximum and minimum points

The sine function (y=\sin(x)) has a maximum at (x = 90^{\circ}) (where (\sin(90^{\circ})=1)) and a minimum at (x = 270^{\circ}) (where (\sin(270^{\circ})=-1)). For (y = 2\sin(x)), when (x = 90^{\circ}), (y=2\times1 = 2) (coordinate ((90^{\circ},2))); when (x = 270^{\circ}), (y=2\times(-1)=-2) (coordinate ((270^{\circ},-2)))

Answer:

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

To graph the function, plot these key points and draw a smooth sine - wave curve passing through them within the interval (0^{\circ}\leq x\leq360^{\circ}). Label the x - axis as "Angle (degrees)" and the y - axis as "y - value".