Simplify sin(180+x)

Problem

sin(180+x)

Solution

1. Identify the appropriate trigonometric identity for the sine of a sum of two angles.

2. Apply the formula sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B) where A=180 and B=x

sin(180+x)=sin(180)*cos(x)+cos(180)*sin(x)

3. Evaluate the known trigonometric values for the specific angle 180

sin(180)=0

cos(180)=−1

4. Substitute these values back into the expanded expression.

sin(180+x)=(0)*cos(x)+(−1)*sin(x)

5. Simplify the resulting expression by performing the multiplication and addition.

sin(180+x)=−sin(x)

Final Answer

sin(180+x)=−sin(x)

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