Verify the Identity sin(x+2pi)=sin(x)

Problem

sin(x+2*π)=sin(x)

Solution

1. Identify the sum formula for the sine function, which is sin(α+β)=sin(α)*cos(β)+cos(α)*sin(β)

2. Substitute the values α=x and β=2*π into the sum formula.

sin(x+2*π)=sin(x)*cos(2*π)+cos(x)*sin(2*π)

3. Evaluate the trigonometric constants using the unit circle, where cos(2*π)=1 and sin(2*π)=0

sin(x+2*π)=sin(x)*(1)+cos(x)*(0)

4. Simplify the expression by performing the multiplication and addition.

sin(x+2*π)=sin(x)+0

sin(x+2*π)=sin(x)

Final Answer

sin(x+2*π)=sin(x)

Want more problems? Check here!