What is the integral of sin(x-pi/2) ?

The integral of sin(x-pi/2) is -sin(x)+C

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integral of sin(x-pi/2)

\int sin (x - \frac{π}{2}) d x

- sin (x) + C

Solution steps

\int sin (x - \frac{π}{2}) d x

Rewrite using trig identities

= \int - cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= - sin (x)

Add a constant to the solution

= - sin (x) + C

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