Simplify sin(2pi-x)

Problem

sin(2*π−x)

Solution

1. Identify the trigonometric identity for the sine of a difference, which is sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

2. Substitute the values A=2*π and B=x into the identity.

3. Evaluate the known trigonometric values for the angle 2*π where sin(2*π)=0 and cos(2*π)=1

4. Simplify the resulting expression by performing the multiplication.

0⋅cos(x)−1⋅sin(x)

−sin(x)

Final Answer

sin(2*π−x)=−sin(x)

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