The function y = 3sin (2x + π / 6) is the closest axis of symmetry to the Y axis

The function y = 3sin (2x + π / 6) is the closest axis of symmetry to the Y axis

The axis of symmetry of a sine function is the point where the function gets the minimum and maximum
So 2x + π / 6 = π / 2 + 2K π or 2x + π / 6 = - π / 2 + 2K π
X = π / 6 + K π or x = - π / 3 + K π
So the nearest axis of symmetry to the y-axis is x = π / 6
The axis of symmetry of a sine function is the point where the function gets the minimum and maximum,
2X + π / 6 = π / 2 + K π, so x = π / 3 + K π / 2,
When k = - 1, x = - π / 6 is the solution.
The function f (x) = asin (Wx + b) (a > 0, w > 0,0) is known
f(1)+f(2)+...+f(2011)
（1）f(x)=2sin(πx/4 + π/4)
（2）2+√2
The maximum value is 2, i.e. a = 2;
If the distance between two adjacent symmetrical axes of an image is 4, that is, t / 2 = 4, then t = 8 = 2 π / W, so w = π / 4;
The image passes through points (1,2), that is, f (x) = 2, that is, 2Sin (π / 4 * 1 + b) = 2, sin (B + π / 4) = 1, B = π / 4
So, f (x) = 2Sin (π X / 4 + π / 4)
(2) The period is 8. In a period, that is, the sum of the function values obtained from 8 consecutive integer points is just 0
f(1)=2,f(2)=√2,
f(3)=0,f(4)=-√2,f(5)=-2,f(6)=-√2,f(7)=0,f(8)=√2,f(9)=2,f(10)=√2,
f(11)=0,
……
f(2011)=0
That is, f (3) + F (4) + F (5) + F (6) + F (7) + F (8) + F (9) + F (10) = 0,
2011-2=2009,
2009/8=251…… 1,
So, f (1) + F (2) +... + F (2011) = f (1) + F (2) + +0*251+f(2011)=2+√2
(1) A = 2
Period T = 2pi / W, then t / 2 = 4, t = 8
So w = pi / 4
After (1,2), the substitution is simplified as sin (PI / 4 + b) = 1, PI / 4 + B = pi / 2 + 2kpi
Again, 0
How about the log image with 2 as the base and 3-x as the logarithm
log[2][-(x-3)]
F (- x) and f (x) are symmetric about the Y axis
So: the image of log2 (- x) and log2 (x) are symmetric about the Y axis
F (x-a) = f (x) right shift a
So log2 (- (x-3)) = log (- x) shifts right by 3
So the logarithmic image of log23-x is the image of log23-x made symmetrically about the Y axis, and then shifted 3 units to the right
If the function y = - 2x + B + 3 is a positive proportional function, then B=
b+3=0
b=-3
If the function f (x) = log takes a as the base x logarithm (a > 0, a ≠ 1) of the image passing through the point (2,1 / 4), find f (8)
It is known that loga (2) = 1 / 4, so 2 = a ^ (1 / 4), then a = 16,
So f (8) = log16 (8) = log2 (8) / log2 (16) = 3 / 4
Cubic meter ^Draw the image of the following positive scale function (I only want the coordinates) y = 4x. Y = 2x out of 3. Y = 2x out of 3
It is known that the angle between the unit vectors m and N is 60. It is proved that (2n-m) is perpendicular to m and its geometric meaning is explained,
2n-m and m are two right angle sides of right angle three solutions respectively. The hypotenuse should be 2m. But why is 2n written on the picture on page 132 of the textbook?
∵ (2n-m) & ﹥ 8226; m = 2n & ﹥ 8226; M-M & ᦇ 178; = 2 | m | & ᦇ 8226; | n | cos 60 ° - | m | & ᦇ 178; = 1-1 = 0 ∧ (2n-m) ⊥ m from the triangle of vector subtraction, 2n, m, 2n-m form a triangle, ∵ (2n-m) ⊥ m ∧ form a right triangle with (2n-m), m as the right edge and 2n as the hypotenuse
As shown in Figure 1, the line y = - 3 / 4x + 3 intersects the x-axis at point a, and the line y intersects the y-axis at point B, and the line y intersects the positive scale function y = 3 / 4x
Intersection at point C
(1) Find the length of line ab
(2) Find the coordinates of the intersection point C
(3) As shown in Figure 2, make a vertical line L of X axis through C. point P is a point on L and is located in the first quadrant. Let the ordinate of point p be a
【1】 When the point P is above the point C, connect AP and BP to find the analytic function of the area s of the triangle PAB with respect to a;
【2】 If the triangle PAB is a right triangle, then a = (write the answer directly)
The second grade of junior high school
(1) In the case of y = - 3 / 4x + 3, which is the result of y = 3, that is, B (0,3) and (3,3) in the case of B (0,3,3) (3) and (3,3,3) in the case of B (0,3,3) - 3, that is, B (0,3) 3 (3,4,4x + 3-3) by the substitution of y = 0 into y = - 3 / 3 / 4x + 3, and the case of B (4,4,4,4,4,4,4 + 3) in the case of B (3,3,4,4,4,4,4,4,4,4,4,4,4x + 4x + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3-4x + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3-3-3-3-3-3-3 and y = 3 / 4x are solved at the same time: & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; &The & nbsp; & nbsp & nbsp; & nbsp & nbsp; & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & nbsp; & nbsp& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; &It's been three-year-3-2 + 4a-12, and it's been three-year-3-2 + 4a-12-12, and it's been one of the first three-year-4-and it's been four-year-4a-4-4-12, and it's been one of the three-year-12-12-12-12, and it's been three-and-we're going to be a-4-12-12-12-12-12-12-12-12-12, and it will be four-4a-4a-4-4-4-4-4-4-12-12-12-12-12-4-4-4-4-4-12-4-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-12-sp; a & gt; 3 / 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; &The distance from P to AB is (4a-6) / 5 & nbsp & nbsp; & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; &According to the formula of the distance between two points, the two-point distance formula can be: & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; from the formula of the distance between two points, the formula from the formula of the two-point distance formula is: & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp & nbsp; & & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & & nbsp; & nbsp; & & nbsp; & & nbsp; & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & nbsp= √ [(2-0) &# 178; + (A-3) &# 178;] = √ (A & # 178; - 6A + 13) & nbsp; & nbsp; &The & nbsp; & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp; & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp; & nbsp; & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp; & & nbsp& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; &The & nbsp & nbsp; & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & nbsp & & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; substituting PA, Pb and ab into, The first part of the solution is: & & nbsp; & & nbsp; & nbsp; & & nbsp; & nbsp; & & nbsp; & & nbsp; & & nbsp; & amp & nbsp; & amp & amp & nbsp; & amp & amp & nbsp; & amp & nbsp; & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & & nbsp; & nbsp; & amp & amp & amp & amp & amp & nbsp; & amp & amp & amp & amp & amp & amp & nbsp; & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & amp & nbsp; & amp & amp & amp & amp & amp & amp & amp & nbsp; & amp & amp & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp;                                       
It is said in the book that the algorithm of positive integer exponential power is also applicable to integer exponential power, but in the algorithm of positive integer exponential power, a ^ m / A ^ n = a ^ M-N (M > n)
However, M-N in integer exponential power may be less than 0, so it does not meet the requirement of (M > n),
The algorithm of positive integer exponential power is also suitable for integer exponential power without m > n
A ^ 2 / A ^ 3 = 1 / A is OK. If a is 0, it won't work
What are the common points of images with positive scale function y = - 4x, y = 4x, y = 1 / 4x
The angle between (0,0) origin and coordinate axis is the same