The image of function y = 2Sin (2x + π / 6) can be obtained by which unit the image of function y = 2sin2x is shifted

The image of function y = 2Sin (2x + π / 6) can be obtained by which unit the image of function y = 2sin2x is shifted

The translation is for the independent variable x, then the original function y = 2sin2x, you can do this transformation y = 2Sin (2 (x + pi / 12)) to get the function you want
So we should move pi / 12 units to the left along the x-axis
It's important to understand how many units of translation along the X axis are for X, not 2x
Welcome to ask~

If the area of the triangle formed by the line y = KX + 2 and the two coordinate axes is 6, finding the value of K is a process and a thought. Thank you

y=kx+2
Let x = 0 be y = 2
Let y = 0 give x = - 2 / K
Because the area of the triangle formed by the line y = KX + 2 and the two axes is 6
SO 2 * | - 2 / K | / 2 = 6
So | K | = 1 / 3
So k = ± 1 / 3

Given that the area of the triangle formed by the line y = KX - 3 and the two coordinate axes is 6, the value of K is obtained

As shown in the figure, let y = kx-3 = 0 get x = 3k, then the coordinates of the intersection of the line y = kx-3 and the X axis are (3k, 0), that is, a (3k, 0), let x = 0 get y = - 3, then the coordinates of the intersection of the line y = kx-3 and the Y axis are (0, - 3), that is, B (0, - 3). Method 1: when k > 0, the solution is k = 34 from s △ AOB = 12 · Ao · Bo = 12 · 3K · 3 = 6; when k < 0, the solution is k = - 34 from s △ AOB = 12 · Ao · Bo = 12 · (- 3K) · 3 = 6 Method 2: from s △ AOB = 12 · Ao · Bo = 12 ·| 3K ·| · 3 = 6, k = ± 34