It is known that the minimum period of function f (x) = asin (2 ω x + π / 6) + A / 2 + B (x ∈ R, a ＞ 0, ω ＞ 0) is π, and the maximum value of function f (x) is 7 / 4 It is known that the minimum period of function f (x) = asin (2 ω x + π / 6) + A / 2 + B (x ∈ R, a > 0, ω > 0) is π, and the maximum value of function f (x) is 7 / 4, The minimum value is 3 / 4 (1) find the value of a B ω (2) point out the monotone increasing interval of F (x) (3) point out the set of X when f (x) gets the maximum and minimum value

It is known that the minimum period of function f (x) = asin (2 ω x + π / 6) + A / 2 + B (x ∈ R, a ＞ 0, ω ＞ 0) is π, and the maximum value of function f (x) is 7 / 4 It is known that the minimum period of function f (x) = asin (2 ω x + π / 6) + A / 2 + B (x ∈ R, a > 0, ω > 0) is π, and the maximum value of function f (x) is 7 / 4, The minimum value is 3 / 4 (1) find the value of a B ω (2) point out the monotone increasing interval of F (x) (3) point out the set of X when f (x) gets the maximum and minimum value

The minimum is - A + A / 2 + B = 3 / 4
The maximum is a + A / 2 + B = 7 / 4
a=1/2 b=1
2π/2w=π w=1
2 f(x)=1/2*sin(2x+π/6)+5/4
Monotone increasing interval 2x + π / 6 in [2K π - π / 2,2k π + π / 2]
The results show that x is in [K π - π / 6, K π + π / 3]

Given that sin (30 ° + 120 °) = sin30 °, can we say that 120 ° is a period of sine function y = SiNx

If we want to show that 120 ° is a period of sine function y = SiNx, then we should not only satisfy sin (30 ° + 120 °) = sin30 ° at 30 ° but also satisfy sin (x + 120 °) = sinxx at any angle. If the above formula holds, then 120 ° is a period of sine function y = SiNx

Is it true that sin (30 + 120) = sin30? If so, can we say that 120 degrees is the period of sine function y = SiNx?

No, because the period needs to conform to f (x + T) = f (x), X can take any value in the definition field, take a good look at the book, be careful not to fail