Find the Exact Value sin(10pi)

Problem

sin(10*π)

Solution

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

2. Determine the number of full rotations. The value 10*π can be written as a multiple of 2*π

(10*π)/(2*π)=5

3. Rewrite the expression using the periodicity property. Since 10*π is an even multiple of π it is coterminal with 0

sin(10*π)=sin(0+5⋅2*π)

sin(10*π)=sin(0)

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

sin(0)=0

Final Answer

sin(10*π)=0

Want more problems? Check here!