Maximum value of $5\sin x - 12 \cos x + 1$ Given that $5\sin x - 12\cos x = 13\sin (x-67.4)$ 
Find the maximum value of $5\sin x - 12 \cos x + 1 $ and the corresponding value of x from 0 to 360. 
Maximum value = $13+1=14$ 
Corresponding value of $x$ 
$13\sin (x-67.4) + 1 = 14$ 
$\sin(x-67.4) = 1 $
$x = 157.4 , 337.4 $ 
I found the value of $x$ and there’s 2 values. However , the answer is only$157.4$ why is that the case ? 

Note that we have the maximum value for $x-67.4°=90°$ indeed for $x-67.4°=270°$ we have that $\sin=-1$ is minimum.
