Express (x)=½ cos (x+ pi) as a sine function.

Answer 1

To express \(f(x)=\frac{1}{2}\cos(x + \pi)\) as a sine function, we can utilize the identity \(\sin(x+\pi/2)=\cos(x)\).

Starting with \(f(x)=\frac{1}{2}\cos(x + \pi)\), we can write \(f(x)=\frac{1}{2}\cos((x + \pi) + \pi/2)\).

By applying the identity, we get \(f(x)=\frac{1}{2}\sin((x + \pi) + \pi/2 + \pi/2)\).

Simplifying the expression inside the sine, we have \(f(x)= \frac{1}{2}\sin(x+2\pi)\).

Finally, simplifying further, we obtain the desired sine function: \(f(x)=\frac{1}{2}\sin(x)\).