Sorry about that,do you think it would be easier to explain with graphs?
plot 1 - sqrt(5)sin (x+26.57) - Wolfram|Alpha
plot - (2 sin x+ cos x) - Wolfram|Alpha
1 - sqrt(5)sin (x+26.57)
What we can do now is to decide for sin (x+26.57) to be maximum or minimum and that's by equating it to 1 and -1 because the maximum or minimum depends on sin (x+26.57). There is nothing else we can alter in the expression other than that.
Also,i've heard about cases with ^2(power) and to find the minimum value we have to equate it to 0 as 0^2 = 0 whilst 1 or (-1)^2 will give you a bigger value than if you were to equate it to 0.