The word **angle** , which comes from the Latin word **angŭlus** , refers to a mathematical figure within the area of **geometry** that is formed from two **lines** when they **intersect** each other on the same surface. The angle then is the region of the plane that is between two **rays** or sides that have the same origin or vertex. These angles can be measured in specific **units** and with different measurements as a result and depending on them, they receive a certain **classification** , and it is important to clarify that the measurement of the angles will always be made in **degrees** .

## What are complementary angles?

Complementary angles are the kind of angle that when **added together** make a total of **90 degrees** . When the angles are complementary they are **measured** with the **right angles** .

- Definition
- features
- How to find complementary angles
- Trigonometric functions of complementary angles
- Examples

## Definition

In order to know and understand the meaning of the term complementary angles, we must first know the **etymological** origin of the words that form it. The word angle is of **Greek** origin , which derives from the word * “ankulos”* , which means

**. Then it spread to Latin in the form of ”**

*“crooked”***angulus**” with the meaning of

**.**

*“angle”*On the other hand, the word complementary is of **Latin** origin . It is born from the sum of several very well differentiated parts: the prefix * “com-”* , which means

**; the verb**

*“union”**, which is synonymous with*

**“plere”***;*

**“fill”***, which can be defined as*

**“-Ment”***, and finally, the suffix*

**“medium”****. The latter is used to indicate**

*“-ary”***.**

*“relative to”*That said, it is important to also remember that the angles have different **measures** and that depending on them, the angles receive their **name** and **classification** , in this way, we can say that the complementary angles are those angles that together add up to **90 degrees** (90º).

## features

The main characteristics of the complementary angles are the following:

- Whether they are consecutive or not, they will always add mathematically to
**90 degrees**. - It may be that the angles are not
**together**but if between two angles they manage to make the**sum**of 90 degrees, then they will be complementary. - When two angles add up to
**90 degrees**, then those angles are considered to**complement**each**other**. - They are angles that add up to the measure of a
**right angle**. - Complementary angles are also composed of
**two sides**and**a vertex**at the origin each. - It is important to know the complementary angles because we can find them in many forms in
**nature**and in many**physical phenomena**. - They can be used in
**architecture**,**construction**,**physiognomy**, etc. - Two angles do not need to be
**adjacent**to be**complementary**.

## How to find complementary angles

Remembering that complementary angles are those that when added together give **90 degrees** or **π / 2 rad** . Assuming that we have two angles: α = 50⁰ and β = 40⁰, if we add them we will get 90 °, therefore, we say that the angles complement each other. For example, in a **right triangle** , the sum of the internal angles is equal to 180 °, therefore, we say that in the right triangle the **acute angles** are considered complementary.

## Trigonometric functions of complementary angles

The **trigonometric functions** are functions that have been established for the purpose of extending the **reasons** the numbers **real** and **complex** . These functions are very important in various areas such as **physics , astronomy , cartography and telecommunications** . They are generally defined as the **quotient** between the **sides** of a right triangle and their relationship to the **angles**. In the case of complementary angles, let β be the complementary angle of α, where β = 90º – α, the trigonometric ratios of the complementary angle can be obtained as a function of the trigonometric ratios of **α.**

The trigonometric ratios of the complementary angles are then the following:

**Sine**of the complementary angle:

**sin (90 ° – α) = cos α**

**Cosine**of the complementary angle:

**cos (90 ° – α) = sin α**

**Tangent**of the complementary angle:

**Tan (90 ° – α) = cot α**

**Cosecant**of the complementary angle:

**csc (90 ° – α) = sec α**

**Secant**:

**sec (90 ° – α) = csc α**

**Cotangent**of the complementary angle:

**cot (90 ° – α) = tan α**