Simplify sin(theta)+sin(theta+2pi)+sin(theta+4pi)

Problem

sin(θ)+sin(θ+2*π)+sin(θ+4*π)

Solution

1. Identify the periodicity of the sine function, which states that sin(x+2*k*π)=sin(x) for any integer k

2. Apply the property to the second term sin(θ+2*π) noting that k=1

sin(θ+2*π)=sin(θ)

3. Apply the property to the third term sin(θ+4*π) noting that 4*π=2*(2*π) so k=2

sin(θ+4*π)=sin(θ)

4. Substitute these simplified terms back into the original expression.

sin(θ)+sin(θ)+sin(θ)

5. Combine the like terms to find the final sum.

3*sin(θ)

Final Answer

sin(θ)+sin(θ+2*π)+sin(θ+4*π)=3*sin(θ)

Want more problems? Check here!