Given the function f (x) = sin (2x + 6 / 6) + sin (2x - 6) - 2cos square x, find the function range and minimum positive period and monotone interval

Given the function f (x) = sin (2x + 6 / 6) + sin (2x - 6) - 2cos square x, find the function range and minimum positive period and monotone interval

Let f (x) = cos (2x Pai / 3) sin ^ 2 x? 1: find the value range and minimum positive value of F (x), so the value range is [1 / 2-radical 3 divided by 2, 1 / 2 radical sign 3 divided by 2], and the minimum positive circumference is π

Let f (x) = 2cos (π / 4-x) + sin (2x + π / 3) - 1, X ∈ R Let f (x) = 2cos (π / 4-x) + sin (2x + π / 3) - 1, X ∈ R Find the minimum positive period When x ∈ [0, π / 2], find the function range

f（x）=2cos^2(π/4-x)+sin(2x+π/3)-1
=1+cos(π/2-2x)+1/2sin2x+√3/2cos2x-1
=sin2x+1/2sin2x+√3/2cos2x
=3/2sin2x+√3/2cos2x
=√3sin(2x+π/6)
t=2π/2=π
X in [0, π / 2]
2X + π / 6 in [π / 6,7 π / 6]
The value range of function f (x) [- √ 3 / 2, √ 3]

Given f (x) = sin? X + √ 3sinxcosx + 2cos? X, find the minimum positive period of function f (x)

f(x)=1/2*(1-cos2x)+√3/2*sin2x+(1+cos2x)
=√3/2*sin2x+1/2*cos2x+3/2
=sin(2x+π/6)+3/2
So the minimum positive period T = 2 π / 2 = π

Given the function f (x) = sin? 2x + √ 3sinxcosx + 2cos? X, X ∈ R, find the minimum positive period of function f (x) and find the maximum of function f (x) The set of X corresponding to the maximum value of sum

f(x)＝sin²x＋√3sinxcosx＋2cos²x
＝sin²x＋√3sinxcosx＋cos²x＋cos²x
＝1＋√3sinxcosx＋cos²x
＝1＋√3／2 sin2x＋(2cos²x－1＋1)／2
＝1＋√3／2 sin2x＋cos2x／2 ＋1／2
＝3／2＋sin(2x＋ π／6)
The minimum positive period of the function f (x) is t = 2 π / 2 = π
When 2x + π / 6 = π / 2 + 2K π, the maximum value of the function is 5 / 2, and x = π / 6 + K π
In conclusion, the minimum positive period of function f (x) is π;
The maximum value is 5 / 2;
X = π / 6 + K π (K ∈ z)

Find the monotone interval (2x) of (2x) = (2x) if (2x) is a monotone interval Do you want to intersect with the result of the first question? I just learned this and didn't understand it,

1, find the increasing interval of F (x), 2K π - π / 2

Let f (x) = cos (2x + π / 3) + sin ^ 2 x 1. Find the maximum value and minimum positive period of the function. 2. Let a, B, C be the three internal angles of △ ABC, If cos β = 1 / 3, f (C / 2) = - 1 / 4, and C is an acute angle, find Sina

It can be obtained by simplifying it
f(x)=1/2-√3/2 *sin2x
1. Therefore, the maximum value is (1 + √ 3) / 2
The minimum positive period is π
2. F (C / 2) = - 1 / 4
sinC=√3/2
Because C is an acute angle
So C is π / 3
sinA=sin(π-B-C)=sin(2π/3-B)=(√3+2√2)/6

Given the function f (x) = 2cos (π / 3-x / 2), find the monotone increasing interval of F (x)

The definition domain of function is all real numbers R
It is an increasing function when - π + 2K π≤ π, 3-x, 2 ≤ 2K π
Solution 2 / 3 π - 4K π ≤ x ≤ 8 / 3 π - 4K π
So the monotone increasing interval of the function is 2 / 3 π - 4K π ≤ x ≤ 8 / 3 π - 4K π
Enjoy your study

Mathematics of senior one: find the minimum positive period of F (x) by known function f (x) = sin × * sin (x + π / 2) - √ 3cos2 (3 π + x) + √ 3 / 2 (1) (2) Find the equation of symmetry axis of F (x) image and the coordinates of symmetry center and symmetry center Before tonight, overdue void, specific answer, thank you!

f(x)=sin×*sin(x+π／2）－√3cos2(3π+x）+√3／2 =sin×*sin(π／2-x）－√3cos2x+√3／2 =sin×cosx－√3cos2x+√3／2 =1/2sin2x-√3cos2x+√3／2 =sin(2x-π／3)++√3／2
Minimum positive period T = 2 π / 2 = π
Symmetric cycle equation 2x - π / 3 = 2K π + π
X = k π + 2 π / 3 can be substituted by other solutions

Let f (x) = 2 to the power of sin (2x - π / 4). Ask if this function is a periodic function? Find the monotone increasing interval and the maximum value

(1) Because g (x) = sin (2x - π / 4) is a periodic function, H (x) = 2 ^ x is defined as R, so the composite function f (x) = 2 ^ [sin (2x - π / 4)] is also a periodic function, and the period and G (x) are both ω = 2 π / 2 = π. (2) a monotone increasing range of function g (x) is - π / 2 ≤ 2x - π / 4 ≤ π / 2, - π / 4 ≤ X

Function y = sin ^ 2x + 2sinxcosx + 3cos ^ 2x 1 find the minimum positive period of the function 2 find the monotone increasing interval 3 of the function when x takes what value, the function takes the maximum value

The minimum positive period is 2 π / 2 = 2 π / 2 = π / 2 = π / 2 ∈ [2K π - π / 2] x / 2] x ∈ [K π - π / 4] ∈ [2K π - π / 4] ∈ [2K π - π / 2,2k π + π / 2] x ∈ [K π - 3 π / 8, K π + π + π / 8] the monotone decreasing area is [K π - 3 π / 8, K π + π / 8] monotone decreasing region [K π - 3 π / 8, K π + π / 8] monotone decreasing area [K π [K π - 3 π - 8], K π + π + π / 8] monotone decreasing area