In order to get the image of the function y = cos (2x + π / 3), just move the image of function y = sin2x. Thank you for your help

In order to get the image of the function y = cos (2x + π / 3), just move the image of function y = sin2x. Thank you for your help

y=cos(2x+π/3)=sin(2x+n/3+ π/2) =sin(π/2+2x+π/3) =sin(2x+5π/6) =sin[2(x+5π/12)]

The function f (x) = sin (2) 3x+π 2)+sin2 In the image of 3x, the distance between two adjacent symmetry axes is () A. 3π B. 6π C. 3 2 pi D. 3 4 pi

The function f (x) = sin (2)
3x+π
2)+sin2
3x=cos2x
3+sin2x
3=
2sin（2x
3+π
4) The period of the function is 2 π
Two
3=3π，
Therefore, the distance between two adjacent symmetry axes in the image of the function is the length of half a period, which is 3 π
2，
Therefore, C

In the image with y = 2 / 3 + cos (2 / 3 + π), the distance between the two adjacent symmetry axes is

Y = sin (2 / 3x) + (√ 3 / 2) cos (2 / 3x) - (1 / 2) sin (2 / 3x) = (1 / 2) sin (2 / 3x) + (√ 3 / 2) cos (2 / 3x) = sin (2 / 3x + π / 3)

In the image with F (x) = sin2x / 3 + cos2x / 3, the distance between two adjacent symmetry axes is A3π B4π/3 C3π/2 D7π/6

f(x)=√2(2x/3+π/4)
T=2π/（2/3）=3π
So the shortest distance = t / 2
Select c

Y = sin2 / 3x + cos (2x / 3) + cos (2x / 3 + π / 6)

Y = sin2 / 3x + cos2x / 3 + cos2x / 3 * radical 3 / 2-sin2x / 3 * 1 / 2 = 1 / 2sin2x / 3 + (radical 3 / 2 + 1) cos2x / 3 = radical [1 / 4 + (radical 3 / 2 + 1) ^ 2] sin (2x / 3 + @) where the minimum positive period T = 2pai / (2 / 3) = 3pai, so the distance between two adjacent symmetry axes in the image is half period, that is, t / 2 = 3pai / 2

The function y = cos (4x + π) 3) The distance between two adjacent symmetry axes of the image is () A. π Eight B. π Four C. π Two D. π

For y = cos (4x + π)
3)，T=2π
4=π
Two
The distance between two adjacent symmetry axes is t
2=π
Four
Therefore, B

If the function y = cos (2wx + π / 3) (W is greater than 0), the distance between the two adjacent symmetry axes is 2 molecules π, then W=

The period of y = cos (2wx + π / 3) is π parts of W. you should know that the distance between the adjacent symmetry axes is exactly half of the period, that is, π of 2W, so w = 1

If the function y = cos (Wx + Π / 3) (W > 0) is Π / 2, then w is equal to

If the distance between the adjacent symmetry axes of an image is Π / 2, then its period can be known as π, which is known from the drawing. Then w = 2 π divided by the period π, the answer is 2

How can the graph of function y = sin (2x - (PAI / 3)) change to y = sin2x

y=sin2x=sin[2(x+π/6)-π/3]
So to get y = sin2x, just shift y = sin (2x - π / 3) to the left π / 6 units!

In order to get the image with function y = 2 + sin (2x + π / 6), we only need to translate the image vector of function y = sin2x

y=2+sin(2x+π/6)=2+sin2(x+π/12)
The image with y = sin2x needs to be shifted to the left by π / 12 units and then up by 2 units
The corresponding vector is (- π / 12,2)