Find the Exact Value sin(3pi)

Problem

sin(3*π)

Solution

1. Identify the angle in the unit circle. The angle 3*π is equivalent to 2*π+π

2. Determine the coterminal angle. Since 2*π represents one full revolution, 3*π is coterminal with π

3. Locate the point on the unit circle. The angle π corresponds to the point (−1,0) on the unit circle.

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

5. Extract the value. The ycoordinate at π is 0

Final Answer

sin(3*π)=0

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