arc sine

简明释义

反正弦

英英释义

例句

1.In trigonometry, the arc sine (反正弦) of a number is defined as the inverse function of the sine function.

在三角学中，某个数字的arc sine (反正弦) 被定义为正弦函数的反函数。

2.To find the angle whose sine is 0.5, you can use the formula for the arc sine (反正弦) function.

要找到正弦为0.5的角度，你可以使用arc sine (反正弦) 函数的公式。

3.Using a calculator, you can easily compute the arc sine (反正弦) of any value between -1 and 1.

使用计算器，你可以轻松计算任何介于-1和1之间的值的arc sine (反正弦)。

4.In physics, the arc sine (反正弦) can be used to determine angles in wave motion.

在物理学中，arc sine (反正弦) 可用于确定波动中的角度。

5.The arc sine (反正弦) of -1 is equal to -π/2 radians.

arc sine (反正弦) 的值为-1时等于-π/2弧度。

作文

The concept of the arc sine is fundamental in trigonometry and has numerous applications in mathematics, physics, and engineering. To understand this term better, we must first explore its relationship with the sine function. The sine function, which is often abbreviated as sin, takes an angle as its input and returns a ratio of the length of the opposite side to the hypotenuse in a right triangle. However, what if we want to determine the angle when we know the sine value? This is where the arc sine comes into play. The arc sine, denoted as sin⁻¹ or arcsin, is the inverse function of the sine function. It allows us to find the angle whose sine is a given number. For example, if we know that sin(θ) = 0.5, we can use the arc sine function to find θ. In this case, arc sine(0.5) would yield θ = 30 degrees or π/6 radians. This property makes the arc sine function incredibly useful for solving various problems in trigonometry. In practical applications, the arc sine is frequently used in fields such as physics and engineering. For instance, when dealing with waves or oscillations, understanding the angles involved in sine functions can help engineers design better structures or systems. Additionally, in navigation and computer graphics, the arc sine function assists in determining angles based on coordinate positions. Another important aspect of the arc sine function is its range. While the sine function can output values between -1 and 1, the arc sine function only produces angles within a specific range: from -π/2 to π/2 radians (or -90 degrees to 90 degrees). This restriction ensures that the arc sine function remains a proper function, meaning it can only return one unique angle for each sine value within this interval. When graphing the arc sine function, we observe that it is a curve that passes through the origin and increases steadily, reflecting the relationship between the angle and its sine value. As we approach the limits of -1 and 1 on the sine scale, the arc sine function approaches -π/2 and π/2, respectively. This visual representation helps reinforce our understanding of how the arc sine function behaves and its relationship to the sine function. In conclusion, mastering the concept of arc sine is essential for anyone studying mathematics or related fields. It serves as a bridge between angles and their sine values, allowing us to solve complex problems with ease. By understanding the properties, applications, and graphical representation of the arc sine function, we can enhance our mathematical skills and apply them effectively in real-world situations. Whether it’s in physics, engineering, or navigation, the arc sine function is a powerful tool that enriches our understanding of the world around us.

“弧正弦”这一概念在三角学中是基础，并且在数学、物理和工程等多个领域都有广泛的应用。为了更好地理解这个术语，我们首先需要探讨它与正弦函数的关系。正弦函数，通常缩写为sin，接受一个角度作为输入，并返回直角三角形中对边与斜边的比率。然而，如果我们想在知道正弦值的情况下确定角度呢？这就是“弧正弦”发挥作用的地方。“弧正弦”，记作sin⁻¹或arcsin，是正弦函数的反函数。它允许我们找到一个角度，使得其正弦值为给定的数字。例如，如果我们知道sin(θ) = 0.5，我们可以使用“弧正弦”函数来求解θ。在这种情况下，弧正弦(0.5)将得出θ = 30度或π/6弧度。这一特性使得“弧正弦”函数在解决各种三角问题时极为有用。在实际应用中，“弧正弦”常常用于物理和工程等领域。例如，在处理波动或振荡时，理解正弦函数中涉及的角度可以帮助工程师设计更好的结构或系统。此外，在导航和计算机图形学中，“弧正弦”函数帮助确定基于坐标位置的角度。“弧正弦”函数的另一个重要方面是其范围。虽然正弦函数可以输出-1到1之间的值，但“弧正弦”函数仅在特定范围内产生角度：从-π/2到π/2弧度（或-90度到90度）。这一限制确保了“弧正弦”函数保持为一个适当的函数，意味着它只能为该区间内的每个正弦值返回一个唯一的角度。在绘制“弧正弦”函数的图形时，我们观察到它是一条通过原点并稳定上升的曲线，反映了角度与其正弦值之间的关系。当我们接近正弦范围的-1和1时，“弧正弦”函数分别接近-π/2和π/2。这一视觉表现有助于加强我们对“弧正弦”函数行为及其与正弦函数关系的理解。总之，掌握“弧正弦”的概念对于任何学习数学或相关领域的人来说都是至关重要的。它作为角度与其正弦值之间的桥梁，使我们能够轻松解决复杂的问题。通过理解“弧正弦”函数的性质、应用和图形表示，我们可以增强我们的数学技能，并在现实世界中有效应用它们。无论是在物理、工程还是导航中，“弧正弦”函数都是一项强大的工具，丰富了我们对周围世界的理解。