It is known that the minimum positive period of the function ∫ (x) = sin ^ 2 ω x + radical 3sin (ω x + π / 2) (ω > 0) is π Find the value range of ∫ (x) on the interval [0,2 π / 3]

If f (x) = sin ^ 2, then f (x) = (cos2x) ^ 2 + √ 3sin (ω x + π / 2) = - (COS ω x) ^ 2 + √ 3cos ω x + 1, its minimum positive period is π, therefore, ω = 2, then f (x) = - (cos2x) ^ 2 + √ 3cos 2x + 1 set cos2x = t, because x ∈ [0,2 π / 3], so t ∈ [- 1,1], y = - T ^ 2 + √ 3T + 1 = - (T - √ 3 / 2) ^ 2 + 7 / 4, therefore, t = (T - √ 3 / 2) ^ 2 + 7 / 4, therefore, t = (T - √ 3 / 2) ^ 2 + 7 / 4, so t = (at 3 / 2

Given the function f (x) = radical 3sin (2x - π / 6) = {sin (x - π / 12) 2 (x is R), find the minimum positive periodic symmetric axis monotone interval of 1 function The image of function f (x) can be obtained from the image of y = SiNx

f(x)=SQR(3)sin(2x-π/6)
From y = SiNx, first X is invariant, y becomes larger SQR (3) times, then y is invariant, X is reduced by 2 times
Don't know how to ask questions

1. It is known that the minimum positive period of the function f (x) = sin 2 ω x + Radix 3sin ω xsin [ω x + π / 2] (ω > 0) is π. (1) find the value of ω; 1. It is known that the minimum positive period of the function f (x) = sin 2 ω x + radical 3sin ω xsin [ω x + π / 2] (ω > 0) is π (1) Find the value of ω; (2) Find the value range of function f (x) on the interval [0, 2 π / 3] 2. Vector E1 E2 two mutually perpendicular unit vectors, and vector a = - (2E1 + E2), vector b = E1 - λ E2 If vector a is parallel to vector B, find the value of λ If vector a is perpendicular to vector B, find the value of λ

F (x) = 1 / 2 (1 / 2) cos2wx + (1 / 2) cos2wx + (3 sinwxcoswx = (√ 3 / 2) sin2wx - (1 / 2) sin2wx - (1 / 2) cos2wx + (3 / 3 / 2) sin2wx - (1 / 2) cos2wx + 1 / 2 = sin (2wx - π / 6) + 1 / 2 (1) minimum positive cycle T = 2 π / 2W = π w = π w = 1 (2) x ∈ [0,2 π / 3] 2x - π / 6 ∈ [- π / 6 ∈ [- π / 6 ∈ [- π / 6 ∈ [- π / 6] 6 ∈ [- π / 6 ∈ [- π / 6] 6 ∈ [- π7 π / 6] Si

The known function f (x) = sin2 ω x+ 3sinωxsin（ωx+π 2) The minimum positive period of (ω > 0) is π (1) Find the value of ω; (2) Find the function f (x) in the interval [0, 2 π 3] The value range of

(I) f (x) = 1-cos2 ω x2 + 32sin2 ω x = 32sin2 ω x-12cos2 ω x + 12 = sin (2 ω X - π 6) + 12. ∵ the minimum positive period of the function f (x) is π, and ω ﹥ 0,

The known function f (x) = 3sinπx+cosπx，x∈R． (1) Find the minimum positive period and range of function f (x); (2) Find the monotone increasing interval of function f (x)

（1）∵f(x)＝
3sinπx+cosπx=2(
Three
2sinπx+1
2cosπx)=2sin(πx+π
6)，
The minimum positive period of function f (x) t = 2 π
π = 2, and ∵ x ∈ R,

The known function f (x) = 4cosxsin (x + π) 6)−1 (I) find the minimum positive period of F (x); (II) find f (x) in the interval [- π 6，π 4] Maximum and minimum values on

（Ⅰ）∵f（x）=4cosxsin（x+π
6）-1
=4cosx（
Three
2sinx+1
2cosx）-1
=
3sin2x+cos2x
=2sin（2x+π
6），
The minimum positive period of F (x) is t = 2 π
2=π；
（Ⅱ）∵x∈[-π
6，π
4]，
∴2x+π
6∈[-π
6，2π
3]，
∴-1
2≤sin（2x+π
6）≤1，
-1≤2sin（2x+π
6）≤2．
∴f（x）max=2，f（x）min=-1．

Find the period of the function y = 3sin (2x + 4) and find its monotone decreasing interval

Y = 3sin (2x + 4)
The minimum positive period is 2 π / 2 = π
Monotone decreasing interval:
2x+π/4∈[2kπ+π/2,2kπ+3π/2]
x∈[kπ+π/8,kπ+5π/8]
therefore
The monotone decreasing interval is;
[kπ+π/8,kπ+5π/8] k∈z

The known function f (x) = [(2 radical 3sin ^ 2x-sin2x) * cosx / SiNx] + 1 (1) Finding the definition domain and the minimum positive period of F (x) (2) Find the maximum value of F (x) on the interval [π / 4, π / 2]

(1) The definition domain of F (x) is SiNx ≠ 0, that is, X ≠ K π; if f (x) is equal to - 1 when x = k π, the definition domain can be extended to the whole real number field; f (x) = [2 √ 3sinxcosx-2cos? X] + 1 = √ 3sin2x-cos2x = 2Sin (2x - π / 6); therefore, the minimum positive period of F (x) is 2 π / 2 = π

Given the function f (x) = 2cos (π / 3-x / 2), find the period of monotone decreasing interval of y = f (x)? Given the function f (x) = 2cos (π / 3-x / 2), find the period of monotone decreasing interval of y = f (x) Sorry, is it the known function f (x) = 2cos (π / 3-x / 2), find the monotone decreasing interval and period of y = f (x)? And period, find period

Because of monotonic decreasing, 2K π π / 3-x / 2 2K π + π
2kπ-π/3《-x/2《2kπ+2π/3
4kπ-2π/3《-x《4kπ+4π/3
So 4K π - 4 π / 3
Period T = 2 π / W, w = 1 / 2, so t = 4 π
It can also be seen from the decline interval

Let f (x) = sin (π X / 4 - π / 6) - 2cos ^ π X / 8 + 1 1, find the minimum positive period 2 of F (x), if the function y = g (x) The maximum value of y = g (x) is obtained when x (0,4 / 3) Let f (x) = sin (π X / 4 - π / 6) - 2cos ^ π X / 8 + 1 1. Find the minimum positive period of F (x) If the image of the function y = g (x) and y = f (x) is symmetric with respect to x = 1, find the maximum value of y = g (x) when x (0,4 / 3)

In this paper, the author's (π / 4 / 4-π / 6) - 2cos (π / 8 / 8) + 1 = sin (π / 4) xcos (π / 6) - cos (π / 4) xsin (π / 6) - cos (π / 4) xsin (π / 6) - cos (π / 4) x = √ 3 / 2Sin (π / 4) x-3 / 2cos (π / 4) x = √ 3sin [(π / 4) x - (π / 3)] t = (2 π) / (π / 4) = 8 in the G (G) (g / 4) = 8 in the G (g (g / 4) = 8 in the G (1 / 4) = 8 in the G (1 / 4) = 8, in the G (1 / 4) = 8, in the take any point (x, G (x) of the graph of x)

It is known that the minimum positive period of the function ∫ (x) = sin ^ 2 ω x + radical 3sin (ω x + π / 2) (ω > 0) is π Find the value range of ∫ (x) on the interval [0,2 π / 3]