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Till now you must be familiar with the Pythagorean Theorem but what if you are not given all sides? What if you have an angle and just one side? You can't apply the Pythagorean theorem because it requires **ATLEAST **two sides to find the third side. That is where trigonometric ratios came in. Trigonometric Ratios are the trigonometric functions based on the value of the ratio of sides. These ratios are applied on a right angle triangle. There are three common trigonometric ratios and they are . However, these are not all trigonometric ratios, there are more trigonometric ratios and we will discuss them too in this lesson.

To apply these ratios, you need to understand every element of a right-angle triangle. A right-angle triangle looks like this:

The best way to identify whether the triangle is a right angle triangle or not is to check the angles of the triangle. If one of the angles is equal to degrees that means the triangle is a right-angle triangle. Once you identified that you are working with a right-angle triangle, now let's break the triangle into its sides. There are three different sides of a right-angled triangle and they are:

- Hypotenuse (the longest side and represented by "a")
- Perpendicular (opposite side to the angle)
- Base (Adjacent side to the angle)

In a right triangle, the following trigonometric ratios can be defined:

## Sine

The **sine** of the angle B is the ratio between the length of the **opposite side** and the **hypotenuse** of the triangle.

It is denoted by .

## Cosine

The **cosine** of the angle B is the **ratio** between the length of the **adjacent side** and the **hypotenuse** of the triangle.

It is denoted by .

## Tangent

The **tangent** of angle B is the **ratio** between the length of the **opposite side** and the **adjacent side** of the triangle.

It is denoted by .

## Cosecant

The **cosecant** of angle B is the **inverse** of the **sine** of B.

It is denoted by .

## Secant

The **secant** of angle B is the **inverse** of the **cosine** of B.

It is denoted by .

## Cotangent

The **cotangent** of angle B is the **inverse** of the **tangent** of B.

It is denoted by .

## Easy Trick to Remember all Trigonometric Ratios

The first three trigonometric ratios are the most important ratios. Once you memorize them, memorizing as well as understanding other ratios will be very easy for you. Hence, you need to memorize these trigonometric ratios:

We can write these formula using the first alphabet of the word, for example:

Where,

**P **stands for **Perpendicular,**

**H** stands for **Hypotenuse,**

and **B **stands for **Base**.

Here is a small trick to remember, you need to memorize this line, **"Some People Have Curly Brown Hair Through Proper Brushing"**. Let's break it into three parts, "Some People Have", "Curly Brown Hair", and "Through Proper Brushing". If you notice the first alphabet of these sentences then you might notice that they match with the trigonometric ratios. For example, in the first part, the **"S"** in **some** stands for and **"P"** and **"H" **in the **"People Have"** stands for **Perpendicular** and **Hypotenuse**. In the same way, if you check the first alphabet of the second part (which is "Curly Brown Hair"), the "C" in "**Curly**" stands for and **"B"** and **"H"** in the "**Brown Hair"** stands for **Base** and **Hypotenuse**. Last but not least, the **"T"** in **"Through"** stands for , however, the **"P"** and **"B"** in the **"Proper Brushing"** stands for **Perpendicular** and **Base**.

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