The single increasing interval of the function y = LG sin (2x + π / 2)

The single increasing interval of the function y = LG sin (2x + π / 2)

y=lg[sin(2x＋π/2)]=lg[cos2x)]
Then, as long as the increasing and positive interval of cos2x is determined, using the cosine function image, the increasing interval is obtained as follows:
(K π - π / 4, K π], where k is an integer

The monotone decreasing interval of the function y = LG (COS ^ 2x sin ^ 2x) is

The original formula = lgcos2x = find the decreasing function interval of cos2x in (0,1] according to the same increase difference subtraction of composite function
2kπ

Find the function y = sin (1 / 2x + π / 3), X belongs to the monotone increasing interval of [- 2 π, 2 π]

2K π - π / 2 ≤ X / 2 + π / 3 ≤ 2K π + π / 2, i.e. 4K π - 5 π / 3 ≤ x ≤ 4K π + π / 3, the value of K can only obtain 0, that is, the function f (x) = sin (1 / 2x + π / 3), X belongs to the monotonic increasing range of [- 2 π, 2 π], and the increasing range is [- 5 π / 3, π / 3]

Given function f (x) = cos (2x-5 π / 3) + 2Sin (x - π / 4) sin (x + π / 4) (1) Finding the equation of minimum positive period and symmetry axis of function (2) Find the value range of function f (x) in the interval [- π / 12, π / 2]

F (x) = cos (2x-5 π / 3) + 2Sin (x - π / 4) sin (x + π / 4) = cos (2x-2 π / 3 - π) + cos π / 2-cos2x, the product sum difference formula is: sin α sin β = [- cos (α + β) + cos (α - β)] / 2 = - cos (2x-2 π / 3) - cos2x = sin2xsin2 π / 3-cos2xcos2x = (?)

Given the function f (x) = sin (2x + π / 6) - cos (2x + π / 3) + 2cos ^ 2x, find the value of F (π / 12)

(x) = sin (2x + π / 6) - cos (2x + π / 6) - cos (2x + π / 3) + 2cos (2x) x = 3sin2x / 2 + cos2x / 2-cos2x / 2-cos2x / 2 + 2 + 3sin2x / 2 + 2cos 2x / 1 + 1 = 3 sin2x + cos2x + 1 = 2 (3 sin2x / 2 + cos2x / 2 + cos2x / 2) + 1 = 2Sin (2x + π / 6) + 1F 1F (π / 12) = 2Sin (π / 3) + 1 = 1 = 1 = 2Sin (π / 3) + 1 = 1 = 1 = 2 (π / 12) = 2Sin (π / 3) + 1 = 1 = 1 = 1 = 1 = 1 = 2 3 + 1

Monotone interval of y = sin (2x + π / 4)

∵ y = Sint increases in 〔 - π / 2 + 2K π, π / 2 + 2K π] so that 2x + π / 4 = t  π / 2 + 2K π ≤ 2x + π / 4 ≤ π / 2 + 2K π
-3 π / 8 + K π ≤ x ≤ π / 8 + K π can be decreased by the same principle

Y = sin (- 2x) monotone interval

Monotone decreasing interval: [K π - π / 4, K π + π / 4]
Monotone increasing interval: [K π + π / 4, K π + 3 π / 4]
K is an integer

Find the monotone increasing interval of the function y = sin (1 / 2x + π / 3), X ∈ [- 2 π, 2 π] This is an example, just one step. I don't know why: - π / 2 + 2K π ≤ 1 / 2x + π / 3 ≤ 2K π We obtain - 5 π / 3 + 4K π ≤ x ≤ π / 3 + 4K π, K ∈ Z. How did you change this step?

The increasing interval of the function y = sin [(1 / 2) x + π / 3] is obtained by the inequality: 2K π - π / 2 ≤ (1 / 2) x + π / 3 ≤ 2K π + π / 2. Reason: because the increasing interval of function y = SiNx is [2K π - π / 2,2k π + π / 2], the increasing interval of function y = sin [(1 / 2) x + π / 3] is determined by the inequality: 2K π -

Find the monotone increasing interval of the function y = y = sin (1 / 2x + π / 3)

2kπ-π/2≤1/2x+π/3≤2kπ+π/2,k∈Z.
4kπ-5π/3≤x≤4kπ+π/3,k∈Z.
The monotone increasing interval of the function is [4K π - 5 π / 3,4k π + π / 3], K ∈ Z

When a is greater than 1, the absolute value of 1 minus a = ()

π - 3.14
A-1