Find the maximum, minimum and period of the function y = 3cosx + 4sinx

Find the maximum, minimum and period of the function y = 3cosx + 4sinx

Make a right triangle, the adjacent side of acute angle a is 4, the opposite side is 3, and the hypotenuse is 5. Y = 3cosx + 4sinx = 5 [(3 / 5) cosx + (4 / 5) SiNx] = 5 [sinacosx + cosasinx] = 5sin (x + a) because the maximum value of sin (x + a) is 1 and the minimum value is - 1

The minimum value of the function y = 6 + 3sinx + 4cosx is,

y=6+3sinx+4cosx
=6+5（3/5sinx+4/5cosx）
=6+5（coscsinX+sinccosX）cosc=3/5 sinc=4/5
=6+5sin(x+c)
When sin (x + C) = - 1, the minimum value of Y is 1

1. Given that the maximum value of the function y = 3sinx-4cosx + m is 6, then the minimum value of the function is
2. "A > b > 0" is the condition of the inequality LGA ^ 2-lgb ^ 2 > 0

1, which can be reduced to y = 5sin (x +?) + M 5 + M = 6 to get m = 1
The minimum of Y is - 5 + 1 = - 4
2. Sufficiency is not necessary
If there are inequalities, we can get a > b > 0 or a