arccosine

简明释义

英[ˌɑː.kəʊˈsaɪn]美[ˌɑr.kəˈsaɪn]

反余弦

英英释义

单词用法

同义词

反义词

例句

1.The inverse function of that restricted cosine function is called the arccosine function.

被限定的余弦函数之反函数叫做反余弦函数。

2.The inverse function of that restricted cosine function is called the arccosine function.

被限定的余弦函数之反函数叫做反余弦函数。

3.Returns the arccosine of a number.

返回数字的反余弦值。

4.The value of arccosine(1) is 0 radians.

反余弦(1)的值是0弧度。

5.The arccosine of -1 is π radians.

反余弦(-1)是π弧度。

6.When solving the triangle, we used the arccosine to determine one of the angles.

在解决三角形时，我们使用了反余弦来确定其中一个角。

7.To find the angle whose cosine is 0.5, you can use the arccosine function.

要找到余弦为0.5的角度，可以使用反余弦函数。

8.In trigonometry, the arccosine is often represented as cos⁻¹.

在三角学中，反余弦通常表示为cos⁻¹。

作文

In the realm of mathematics, particularly in trigonometry, the concept of angles and their relationships is fundamental. One important function that arises in this field is the cosine function, which relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. However, there are instances when we need to find the angle itself from a given cosine value. This is where the concept of arccosine (反余弦) comes into play.The arccosine (反余弦) function is the inverse of the cosine function. It takes a value from the range of -1 to 1 and returns an angle in radians (or degrees) that corresponds to that cosine value. For example, if we know that the cosine of an angle is 0.5, we can use the arccosine (反余弦) function to determine that the angle is 60 degrees or π/3 radians. This ability to find angles from cosine values is crucial in various applications, ranging from simple geometry problems to complex engineering calculations.Understanding the arccosine (反余弦) function also requires familiarity with its properties. The function is defined on the interval [-1, 1] and has a range of [0, π] radians (or [0, 180] degrees). This means that for every input value within the specified domain, there is a unique output angle. This uniqueness is essential because it allows us to pinpoint a specific angle for a given cosine value, eliminating ambiguity in our calculations.Moreover, the arccosine (反余弦) function is continuous and monotonically decreasing, which means that as the input value increases, the output angle decreases. This characteristic can be particularly useful when solving trigonometric equations or analyzing functions graphically. By understanding how the arccosine (反余弦) behaves, students and professionals can better navigate the complexities of trigonometry.In practical applications, the arccosine (反余弦) function is often used in physics and engineering to resolve vectors and analyze forces. For instance, when calculating the direction of a force vector, one may need to determine the angle between two vectors. By applying the arccosine (反余弦) function, engineers can accurately compute the necessary angles to ensure that structures are built safely and efficiently.In conclusion, the arccosine (反余弦) function is a vital tool in the study of trigonometry, providing a means to find angles from cosine values. Its properties and applications make it an essential concept for anyone working in fields that involve mathematics, physics, or engineering. As students continue to explore the world of mathematics, mastering the arccosine (反余弦) and its implications will undoubtedly enhance their understanding and problem-solving skills.

在数学领域，特别是在三角学中，角度及其关系的概念是基础。一个在这一领域出现的重要函数是余弦函数，它将直角三角形的角度与邻边与斜边的长度比联系起来。然而，有时我们需要从给定的余弦值中找到角度。这就是arccosine（反余弦）概念发挥作用的地方。arccosine（反余弦）函数是余弦函数的反函数。它接受一个范围在-1到1之间的值，并返回一个与该余弦值对应的角度（以弧度或度数表示）。例如，如果我们知道一个角的余弦为0.5，我们可以使用arccosine（反余弦）函数来确定这个角是60度或π/3弧度。从余弦值中找出角度的能力在各种应用中至关重要，从简单的几何问题到复杂的工程计算。理解arccosine（反余弦）函数还需要熟悉它的性质。该函数在区间[-1, 1]上定义，输出范围为[0, π]弧度（或[0, 180]度）。这意味着，对于每个输入值，在指定的定义域内都有一个唯一的输出角度。这种唯一性是必不可少的，因为它允许我们为给定的余弦值准确地确定一个特定的角度，从而消除计算中的歧义。此外，arccosine（反余弦）函数是连续的且单调递减的，这意味着随着输入值的增加，输出角度会减小。这一特性在解决三角方程或图形分析时尤为有用。通过理解arccosine（反余弦）的行为，学生和专业人士可以更好地应对三角学的复杂性。在实际应用中，arccosine（反余弦）函数通常用于物理和工程中以解析向量和分析力。例如，在计算一个力向量的方向时，可能需要确定两个向量之间的角度。通过应用arccosine（反余弦）函数，工程师可以准确计算必要的角度，以确保结构的安全高效建造。总之，arccosine（反余弦）函数是三角学研究中的一个重要工具，提供了一种从余弦值中找出角度的方法。它的性质和应用使其成为任何从事数学、物理或工程领域的人必不可少的概念。随着学生继续探索数学世界，掌握arccosine（反余弦）及其含义无疑将增强他们的理解和解决问题的能力。