Simplify cos((3pi)/2-x)

Problem

cos((3*π)/2−x)

Solution

1. Identify the appropriate trigonometric identity to use, which is the cosine difference formula: cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

2. Substitute the values A=(3*π)/2 and B=x into the formula.

cos((3*π)/2−x)=cos((3*π)/2)*cos(x)+sin((3*π)/2)*sin(x)

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

cos((3*π)/2−x)=(0)*cos(x)+(−1)*sin(x)

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

cos((3*π)/2−x)=0−sin(x)

cos((3*π)/2−x)=−sin(x)

Final Answer

cos((3*π)/2−x)=−sin(x)

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