Simplify sin(x+pi)

Problem

sin(x+π)

Solution

1. Identify the sum formula for sine, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

2. Substitute A=x and B=π into the formula.

sin(x+π)=sin(x)*cos(π)+cos(x)*sin(π)

3. Evaluate the trigonometric constants cos(π)=−1 and sin(π)=0

sin(x+π)=sin(x)*(−1)+cos(x)*(0)

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

sin(x+π)=−sin(x)

Final Answer

sin(x+π)=−sin(x)

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