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

Problem

cos(x−(3*π)/2)

Solution

1. Identify the angle subtraction identity for cosine, which is cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

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

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

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

cos(x−(3*π)/2)=cos(x)*(0)+sin(x)*(−1)

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

cos(x−(3*π)/2)=0−sin(x)

cos(x−(3*π)/2)=−sin(x)

Final Answer

cos(x−(3*π)/2)=−sin(x)

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