Given the function f (x) = 2Sin (x + π / 3) - 2sinx, X belongs to - π / 2,0 (1) If cosx = √ 3 / 3, find the value of function f (x) (2) Finding the range of function f (x) I'm in a hurry

Given the function f (x) = 2Sin (x + π / 3) - 2sinx, X belongs to - π / 2,0 (1) If cosx = √ 3 / 3, find the value of function f (x) (2) Finding the range of function f (x) I'm in a hurry

f(X)=2sin（X+π/3）-2sinX
=2sinX cos(π/3）+2cosX sin(π/3）-2sinX
=sinX+√3cosX-2sinX
=√3cosX-sinX
=2*[(√3/2)cosX-(1/2)sinX]
=2*[sin(π/3)cosX-cos(π/3）sinX]
=2Sin (π / 3-x) and f (x)
(1) If cosx = √ 3 / 3 and X belongs to [- π / 2,0], then SiNx = - √ 6 / 3
From F (x) = √ 3cosx SiNx = 1 + √ 6 / 3
(2) F (x) = 2Sin (π / 3-x), X belongs to [- π / 2,0],
Then π / 3-x belongs to [π / 3,5 π / 6]
If you draw a graph, you can see that the range of F (x) is [1,2]

The image of the function f (x) = 2Sin (x - π / 3) can be regarded as the translation of the image of F (x) = 2sinx

Move the image to the right π / 3

Find the maximum and minimum value of the function y = - 2sin2x + 2sinx + 1, X ∈ {- π / 6,3 π / 4}, and point out to get the maximum value
The value of X

Formula y = - 2 (sinx-1 / 2) ^ 2 + 3 / 2
When x = - π / 6, the maximum value is 1
When x = π / 2, the minimum value is - 1 / 2

Let f (x) = 3sin (ω x + π / 6), ω > 0, and π / 2 be the minimum positive period
When x ∈ [- π / 12, π / 6], find the maximum value of F (x)

Taking π / 2 as the minimum positive period, it is obvious that ω = 4
If x ∈ [- π / 12, π / 6], then ω x + π / 6 ∈ [- π / 6,5 π / 6]
The maximum value is 3, when ω x + π / 6 = π / 2
The minimum value is - 1.5, when ω x + π / 6 = - π / 6

Let f (x) = 3sin (Wx + π / 6), w > 0, X ∈ (- ∞, + ∞), and π / 4 be the minimum positive period（
Let f (x) = 3sin (Wx + π / 6), w > 0, X ∈ (- ∞, + ∞), and take π / 4 as the minimum positive period (1) to find f (0) (2) to find the analytic expression of F (x) (3) to know f (A / 8 + π / 24) = 9 / 5, to find the value of COS square a

F (0) = 3sin (W0 + π / 6), = 3sin (π / 6) = 3 / 2, and π / 2 is the minimum positive period

Let f (x) = 3sin (Wx + π / 3), w > 0, X ∈ R, and π / 2 be the minimum positive period
(1) Find f (0)
(2) Finding the analytic expression of F (x)
(3) Given that f [(α / 4) + (π / 12)] = 3 / 2, find the value of sin α

F (0) = 3sinpai / 3 = 3 radical 3 / 2
w=2Pai/T=2Pai/(Pai/2)=4
(2)f(x)=3sin(4x+Pai/3)
(3)f[a/4+Pai/12]=3sin(a+Pai/3+Pai/3)=3/2
sin(a+2Pai/3)=1/2
A + 2pai / 3 = 2kpi + Pai / 6 or 5pai / 6
A = 2kpi Pai / 2 or Pai / 6
Sina = - 1 or 1 / 2

Let f (x) = 3sin (Wx + π / 6), w > 0, X belong to (negative infinity, positive infinity), and π / 2 be the minimum positive period
If f (A / 4 + π / 12) = 9 / 5, why is the value of sina positive or negative 4 / 5?

The minimum positive period of F (x) is t = 2 π / w = π / 2
We get w = 4
So f (x) = 3sin (4x + π / 6)
So f (A / 4 + π / 12) = 3sin (a + π / 2) = 3cosa = 9 / 5
So cosa = 3 / 5
So Sina = 4 / 5 or - 4 / 5

It is known that the minimum positive period of the function f (x) = 2Sin ^ 2wx + 2 and 3sinwxsin (PAI Wx) (W > 0) is Pai
1 find the value range of function f (x) in the interval [0,2 / 3]
If a and B are Rui angles. If f (a) = 3, cos (a + b) = root 5 / 5, SINB can be obtained

F (x) = 2Sin ^ 2wx + 2 with sign 3sinwxsin (PAI / 2-wx) (W > 0) = 1-cos2wx + √ 3sin2wx = 2Sin (2wx - π / 6) + 1 minimum positive period T = 2 π / 2W = π w = 1F (x) = 2Sin (2x - π / 6) + 1x ∈ [0,2 π / 3] 2x - π / 6 ∈ [- π / 6,7 π / 6] 2Sin (2wx - π / 6) ∈ [- 1,2] function f (x)

Given that the minimum positive period of the function f (x) = 2Sin (ω x + π 6) (ω > 0) is 4 π, then the image ()
A. On point (π 3,0) symmetry B. on point (5 π 3,0) symmetry C. on line x = π 3 symmetry D. on line x = 5 π 3 symmetry

From the function f (x) = 2Sin (ω x + π 6) (ω > 0), the minimum positive period is 4 π to get ω = 12, from 12x + π 6 = k π to get x = 2K π − π 3, the symmetry point is (2k π − π 3, 0) (K ∈ z), and when k = 1, it is (5 π 3, 0), so B

Given that f (x) is an even function and f (x + 4) = f (4-x), finding its period PS, I can only infer that its axis of symmetry is 4
It is known that f (x) is an even function
And f (x + 4) = f (4-x)
Find its period
PS I can only infer that his axis of symmetry is 4

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