As shown in the figure, point a on the circle moves in a circular motion at a constant speed in a counter clockwise direction. It is known that point a turns around the angle of θ (0 ＜ θ ＜ π) in 1 minute, reaches the third quadrant in 2 minutes, and returns to its original position in 14 minutes to calculate θ

As shown in the figure, point a on the circle moves in a circular motion at a constant speed in a counter clockwise direction. It is known that point a turns around the angle of θ (0 ＜ θ ＜ π) in 1 minute, reaches the third quadrant in 2 minutes, and returns to its original position in 14 minutes to calculate θ

Point a turns around 2 θ in 2 minutes, and π < 2 θ < 32 π. After 14 minutes, it returns to its original position, with ﹤ 14 θ = 2K π, θ = k π 7, and π 2 < θ < 34 π, and ﹤ θ = 47 π or 57 π

Let a (10,0) be the starting point,
The velocity of the projective point m of point P on the y-axis at time t?

Let time be t, then v = 0.2 * cos (T / π)

Calculate the integral ∫ Z DS for the curve, where C is the helix, x = tcost, y = TSINT, z = t (0 ≤ t ≤ t0)
(1/3)[()[(2+t0)^2√(2+t0)^2-2√2

The integral ∫ Z DS for a pair of curves is calculated, where C is a helix, x = tcost, y = TSINT, z = t (0 ≤ t ≤ t0)
C：x=tcost,y=tsint,z=t；dx/dt=cost-tsint；dy/dt=sint+tcost；dz/dt=1；
[C]∫z ds=[C]∫t√[(cost-tsint)²+(sint+tcost)²+1]dt
=[C]∫t√[(cos²t-2tsintcost+t²sin²t)+(sin²t+2tsintcost+t²cos²t)+1]dt
=[C]∫t√(t²+2)dt=(1/2)∫√(t²+2)d(t²+2)=(1/2)(2/3)(t²+2)^(3/2)︱[0,to]=(1/3)[(t²o+2)^(3/2)- 2√2]

Sint / 1-cost = what

Sin t = 2 sin half t times cos half t
1-cost = 2 (sin half T) power
One ratio of the two = t / 2 of cot

What do T1 and T2 represent in the linear parametric equation? Why | T1-T2 | is equal to chord length?

When x = x0 + tcosa
When y = Y0 + Tsina
In the linear parametric equation, T1 and T2 represent the number of points (x0, Y0) from the fixed point to the two intersections of the line and curve (that is, there is length and direction), so no matter the fixed point is between or outside the two intersections, | T1-T2 | is equal to the chord length