Hello donnagirl Originally Posted by
donnagirl If p is a positive real number and 2 sin x = 2 sin(x + p) for every real value of x, what is the smallest possible value for p, in degrees?
How can I show that it really is 360?
Divide by $\displaystyle 2$; then expand $\displaystyle \sin (x+p)$, and say:$\displaystyle \sin x \equiv \sin(x+p)$
$\displaystyle \Rightarrow \sin x \equiv \sin x \cos p + \cos x \sin p$
Then compare the coefficients of $\displaystyle \sin x$ and $\displaystyle \cos x$:$\displaystyle \Rightarrow \left\{ \begin{array}{l} \cos p =1\\ \sin p = 0\end{array}\right .$
And the smallest positive value of $\displaystyle p$ that satisfies these equations is $\displaystyle p = 360^o$
Grandad