Ratios of Trigonometric sides are known as **TRIGONOMETRIC RATIOS**.

In Trigonometry, Trigonometric sides are given special significance. So the ratio’s of these sides automatically became important.

**TRIGONOMETRIC SIDES**

**PERPENDICULAR**

**BASE**

**HYPOTENUSE**

We can make 6 combinations of ratio’s based on above mentioned 3 Trigonometric sides. [Try if you can make more than 6 combinations & comment below]

These 6 ratio’s are TRIGONOMETRIC RATIOS. Special names have been allotted to these ratio’s. Which are:

Previously, we have understood that Trigonometric sides are w.r.t to some angle, which we have called as Trigonometric angle. So here also, Trigonometric ratio’s are w.r.t Trigonometric angle. So \theta , as Trigonometric angle, is placed with Trigonometric ratios.

You will observe that Cosec, Sec & Cot are reciprocal of Sin, Cos & Tan respectively. Refer details in post of “Relation among Trigonometric Ratio’s”.

So, Just remember the Trigonometric ratios of Sin, Cos & Tan only. Rest will come automatically, by doing the reciprocal.

## HOW TO APPROACH QUESTIONS

- We can calculate Trigonometric Ratio’s, if we know the 3 sides of a right-angle triangle.
- If only 2 sides are given. Find the missing side with help of Pythagorean theorem.
- Remember the triplets of Pythagorean theorem. [(3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25) etc].
- Once we know the 3 sides, identify the Trigonometric sides (Perpendicular, Base & Hypotenuse). Same we have already covered in previous post.
- Once, you know the 3 Trigonometric side, apply the formulas to get Trigonometric Ratio’s.

## EXAMPLES

**Q1)** Find the Trigonometric Ratio’s Sin \theta , Cos \theta & Tan \theta for the given triangle ABC.

Firstly, we have to identify the Trigonometric sides **Perpendicular, Base & Hypotenuse**. Refer below animation for the same.

We got,

Perpendicular = 4 (Side Opposite to Trigonometric angle \theta )

Base= 3 (Side between 90 Degree & Trigonometric angle \theta )

Hypotenuse = 5 (Side opposite to 90 Degree angle)

Click here to know, How to identify Trigonometric Sides.

Once, we know the 3 sides, we can use formula’s of Trigonometric Ratio’s.

**Q2)** Find the Trigonometric Ratio’s Sin \theta , Cos \theta & Tan \theta , for the given triangle PQR.

Firstly, we have to identify the 3rd missing side, then only, we can proceed further.

We will use Pythagoras, to find the 3^{rd} missing side.

PQ ^{2} + QR ^{2} = PR ^{2}

5^{2} + 12 ^{2} = PR ^{2}

PR = 13

We got all the 3 sides.

Now, we have to **identify Perpendicular, Base & Hypotenuse**.

PQ is Perpendicular, as it is side opposite to Trigonometric angle \theta .

PQ = Perpendicular = 4

QR is base, as it is between 90 degree angle & Trigonometric angle \theta .

QR = Base= 12

PR is Hypotenuse, as it is opposite to 90 degree \theta .

PR = Hypotenuse = 13

Once, we got the 3 sides, we will apply Trigonometric Ratios Formulas.

## Question for you:

**Q)** Find the Trigonometric Ratio’s Sin \theta , Cos \theta & Tan \theta , for the given triangle ABC.