Find the Exact Value sin(4pi)

Problem

sin(4*π)

Solution

1. Identify the angle in the unit circle. The angle 4*π represents two full revolutions around the circle, as one full revolution is 2*π radians.

2. Determine the coterminal angle. Since 4*π is a multiple of 2*π it is coterminal with 0 radians.

sin(4*π)=sin(0)

3. Locate the coordinates on the unit circle. At the angle 0 the coordinates are (1,0)

4. Apply the definition of the sine function. On the unit circle, sin(θ) is equal to the ycoordinate of the point.

sin(0)=0

Final Answer

sin(4*π)=0

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