The angle of rotation is measured in
radians, not degrees.
这个旋转角是以弧度而不是以度数来衡量的。
In calculus, the derivative of sine function with respect to its input is cosine, when measured in
radians.
在微积分中,正弦函数关于其输入的导数是余弦,这里的角度是以弧度为单位的。
The speed of an object moving along a circular path can be calculated by dividing the arc length traveled by time, expressed in
radians per second.
沿圆周运动的物体的速度可以通过将行进的弧长除以时间(以弧度每秒表示)来计算。
A complete revolution around a circle corresponds to 2π
radians.
绕圆一周对应于2π弧度。
The
radian measure is a natural unit for angles in trigonometry, as it relates the size of an angle directly to the arc it subtends on a circle.
弧度制在三角学中是一种自然的角度单位,因为它直接关联了角度大小与其所在圆上的所对弧长。
The Taylor series expansion of many mathematical functions, such as e^x or sin(x), converge more quickly when x is in
radians.
许多数学函数(如e^x或sin(x))的泰勒级数展开式在x用弧度表示时收敛得更快。
An angle of one
radian corresponds approximately to a central angle that subtends an arc of the same length as the radius of the circle.
一个弧度角大约对应着一个中心角,其所对的弧长大约等于圆的半径长度。
To convert from degrees to
radians, you multiply the degree value by π/180.
将角度转换为弧度,你需要将角度值乘以π/180。
The area of a sector in a circle is given by (θ/2π) * πr², where θ is the angle in
radians.
圆形扇区的面积可用公式(θ/2π) * πr²给出,其中θ为该扇区对应的弧度角。
In physics, the angular frequency of a wave is often measured in
radians per second and represents the rate at which the phase of the wave changes.
在物理学中,波的角频率通常以弧度每秒为单位测量,代表波相位变化的速率。
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