cotan

cotan音标为英 ["kəʊtən]、美 ["kotən]，翻译为“余切”的意思。速记技巧可以将其与“商”同音进行联想记忆。cotan是三角函数中的余切函数，在直角三角形中，余切表示为角B的邻边比上斜边。

cotan的英文词源可以追溯到拉丁语词根cotanto，意为“相反”或“成反比”。这个词后来被引入英语，用来表示三角学中的余切（cotangent）概念。

cotan的变化形式主要有复数形式cotans，过去式和过去分词形式cotanned或者coted，现在分词形式cotening。

相关单词有：tangent（切线）、secant（割线）、coefficient（系数）、counter（反对的）、counteract（反抗）、contrast（对比）、compensate（补偿）、reciprocal（互换的）、antithesis（反义词）和converse（相反的）。这些单词与cotan都有一定的关联，部分单词在词义和用法上可以反映出cotangent的概念。

例如，tangent作为cotan的一个相关单词，意为“切线”，在三角学中表示与角终边相切的直线与角的度数之间的比值。secant也有“割线”的含义，指的是与角两边相交的直线之间的比值。coefficient则表示系数，是数学中用来描述两个量之间关系的数字。

总之，cotan及其变化形式和相关单词在英语中用来表示三角学中的余切概念，并广泛用于数学、物理学和工程学等领域。

常用短语：

1. at a tangent to 与...相切

2. on the cusp of 即将...

3. tangent to sth 与某事物有关联

4. be on the same wavelength 意见一致

5. be at cross-purposes with 与...意见不合

6. be at a 90-degree angle to 与...成90度角

7. be perpendicular to 与...垂直

例句：

1. The two companies are at a tangent to each other"s business, and it"s unclear how they will collaborate in the future.

2. The two countries are on the cusp of signing a trade deal that could transform their relationship.

3. Their relationship has been strained lately, and it seems like they"re constantly at cross-purposes with each other.

4. The two sides are working together on a project that requires them to be on the same wavelength.

5. The two buildings are at a 90-degree angle to each other, and it looks like they"ll never fit together.

6. The two sides are working towards a solution that is perpendicular to their previous disagreements.

英文小作文：

Title: Geometry of Relationships

In life, we encounter relationships that are tangential, intersecting, perpendicular, or even at cross-purposes. These relationships can make us feel confused or even hopeless, but they can also teach us valuable lessons about communication, cooperation, and understanding.

For example, imagine two friends who used to be close, but now they"re at a 90-degree angle to each other in their views on life and their choices. They may argue or even avoid each other, but if they can look past their differences and communicate openly, they might find that they"re still on the same wavelength, even if their paths don"t always converge.

On the other hand, there are relationships that are completely perpendicular, where two people have completely different goals or ways of doing things. This can be frustrating, but it can also provide opportunities for growth and learning if both parties are willing to work together and find common ground.

In any case, relationships are like geometric shapes in that they can be complex and diverse, but they can also be beautiful and enriching if we approach them with an open mind and an attitude of understanding and acceptance.