Find the Exact Value sin(7pi)

Problem

sin(7*π)

Solution

1. Identify the period of the sine function. The sine function has a period of 2*π meaning sin(θ)=sin(θ+2*n*π) for any integer n

2. Reduce the angle by subtracting multiples of the period. We can write 7*π as 6*π+π

3. Apply the periodicity property. Since 6*π is 3×2*π the value of the function is the same as at π

sin(7*π)=sin(π+3*(2*π))

sin(7*π)=sin(π)

4. Evaluate the sine of the resulting angle. On the unit circle, the point corresponding to π radians is (−1,0) The sine value is the ycoordinate of this point.

sin(π)=0

Final Answer

sin(7*π)=0

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