The chord length is 4.9 meters, and the bow height is 0.7 meters

The chord length is 4.9 meters, and the bow height is 0.7 meters

The chord length is L = 4.9 m, the bow height is h = 0.7 m, and the arc length C?
The radius of arc is r, and the center angle of arc is a
R^2=(R-H)^2+(L/2)^2
R^2=R^2-2*R*H+H^2+L^2/4
2*R*H=H^2+L^2/4
R=H/2+L^2/(8*H)
=0.7/2+4.9^2/(8*0.7)
=4.6375m
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((4.9/2)/4.6375)
=78 degrees
C = pi * r * A / 180 = pi * 4.6375 * 63.78/180 = 5.162m

It is known that the chord length of the bow is 7.6m, the arc length is 8.2m, and the arc length is 4m,

Let radius be r, R & # 178; = 3.8 & # 178; + (r-1.4) &# 178;; r = 5.86; sin1 / 2 central angle = 3.8/5.86; central angle = 80.85
S arch = 80.85 / 360 * 3.14 * 5.86 & # 178; - 1 / 2 * 7.6 * 4.46 = 7.27m & # 178;

Find the maximum and minimum of the function y = 7-4sinxcosx + 4cos2x-4cos4x

Y = 7-4sinxcosx + 4cos2x-4cos4x = 7-2sin2x + 4cos2x (1-cos2x) = 7-2sin2x + 4cos2xsin2x = 7-2sin2x + sin22x = (1-sin2x) 2 + 6. Since the maximum value of Z = (U-1) 2 + 6 in [- 1, 1] is Zmax = (- 1-1) 2 + 6 = 10, and the minimum value is Zmin = (1-1) 2 + 6 = 6, the function z = (U-1) 2 + 6 has a maximum value of Zmax = (- 1-1) 2 + 6 = 10 and a minimum value of Zmin = (1-1) 2 + 6 = 6

Given that the coordinates of point P are (x, y), and satisfy (x-1) ² = 4, |y-1 | = 2
(1) Find the coordinates of point P;
(2) If point P is in the second quadrant and the coordinates of point q are (m, n), what are the values of M and n when point PQ ‖ Y axis?

(1)
(x-1)²=4,|y-1|=2.
x-1=±2,y-1=±2
Ψ x = 3 or x = - 1, y = 3 or y = - 1
The P coordinate of the point is
(3,3),(3,-1),(-1,3),(-1,-1)
(2)
(m, n), when the point PQ ‖ Y axis
Then the abscissa of point q is equal to that of point P,
Ψ M = - 1 or M = 3,
The ordinate is not equal to the ordinate of point P,
∴n≠-1,n≠3

The minimum positive period of the function y = 4sin π x is

The minimum positive period of y = 4sin π x is t = 2

What are the periods of y = 2Sin one third x y = 4sin (x - π / 3) y = sin (2x + π / 6) y = 3sin (1 / 2x - π / 4),

Well, you just need to remember the algorithm. Let's take the coefficient of X as w and use 2 π / W

The period of y = sin ^ 2 (2x) + 4sin ^ 4 (x)

y=sin^2（2x）+4sin^4（x）
=sin^2（2x）+[1-cos（2x）]^2
=sin^2（2x）+1-2cos（2x）+cos^2（2x）^2
=2-2cos（2x）
Period T = 2 π / 2 = π
If you don't understand, please ask. If you understand, please select it as a satisfactory answer in time! (*^__ ^*)

Given the function y = 4sin (2x + π / 6), X belongs to R (1) find the minimum positive period of the function (2) write the monotone increasing interval of the function (3) write the symmetry axis of the function

1. Minimum positive period = 2 π / 2 = π
2) The increasing interval satisfies:
2kπ-π/2≤2x＋π/6≤2kπ＋π/2
2kπ-2π/3≤2x≤2kπ＋π/3
That is k π - π / 3 ≤ x ≤ K π + π / 6
The increasing interval is [K π - π / 3, K π + π / 6]
3) The axis of symmetry satisfies:
2x＋π/6=kπ＋π/2
2x=kπ＋π/3
x=kπ/2＋π/6

Given x + y = 3-cos (4a), X-Y = 4sin (2a), find x ^ 1 / 2 + y ^ 1 / 2 = 2

If x + y and X-Y are known, then x = (3-cos4a + 4sin2a) / 2 = (3-2cos & sup2; 2A + 1 + 4sin2a) = (4-2 + 2Sin & sup2; 2A + 4sin2a) / 2 = Sin & sup2; 2A + 2sin2a + 1 = (sin2a + 1) & sup2; y = (3-cos4a-4sin2a) / 2 = (3-2cos & sup2; 2A + 1-4sin2a) = (4-2 + 2Sin & sup2; 2a-4sin2a) /

Simplification: detailed explanation of 4sin π / 4 cos π / 4

4sin π/4 cos π/4
=2 times 2Sin π / 4 cos π / 4
=2sin π/2
=2sin90 degrees
=Two times one
=2
If you don't understand, you are welcome to ask,