# RELATION AMONG TRIGONOMETRIC RATIOS

In previous Lecture, we have studied “Introduction to Trigonometric ratios“and have also seen the formulas of Trigonometric ratios.

Closely, observe the above formulas. Are you able to observe any linkage between Trigonometric Ratios w.r.t. Trigonometric Sides?

Yes, you have observed it correctly. These Trigonometric Ratio’s are linked to each other. Lets see it in detail, how they are linked? And we will come out with new set of Formulas.

## Conclusion:

As per 1st relation, if we know the formula of Sin \theta & Cos \theta , We can calculate the formula of Tan \theta , by simply dividing Sin \theta & Cos \theta .

And we have also found that, Cosec \theta , Sec \theta & Cot \theta are reciprocal of Sin \theta , Cos \theta & Tan \theta respectively.

So, if You know the Formula of Sin \theta , Cos \theta & Tan \theta , you can calculate the formula of Cosec \theta , Sec \theta & Cot \theta ,  Just simply by doing the reciprocals.

## Approach to Solve Questions:

• Calculate the value of Sin \theta & Cos \theta . This may be given in the question OR you can use the basics to calculate the same.
• Divide Sin \theta and Cos \theta , to get Tan \theta .
• Once we know the value of Sin \theta , Cos \theta & Tan \theta , just by doing the reciprocals, we get the value of Cosec \theta , Sec \theta & Cot \theta .
• We got all the 6 Trigonometric Ratios.

Based on these relations, lets try to solve some questions.

## Question:

Q) Sin \theta = \frac { 3 }{ 5 } , Cos \theta = \frac { 4 }{ 5 } . Based on this data, find rest of the Trigonometric Ratios?

In this question, Sin \theta and Cos \theta are given. We have to find rest of the four Trigonometric ratios, which means, we have to find value of Tan \theta , Cosec \theta , Sec \theta & Cot \theta .

Lets approach the question and see how to solve it.

We can find the value of Tan \theta , with help of Sin \theta & Cos \theta . The applicable relation will be:

And once, we know Sin \theta , Cos \theta & Tan \theta , we can easily find Cosec \theta , Sec \theta & Cot \theta , just by doing the reciprocals.

### Alternate Way to Approach Question:

Sin \theta is given as 3/5 and Cos \theta is given as 4/5. Can we say, for a Right angle triangle, Perpendicular is 3, Base is 4 & Hypotenuse is 5. Can we?  [Tell in the comment section, Why?]

Once you know the 3 sides a right angle triangle, you can calculate all the Trigonometric Ratios.  [Show the complete steps in the comment below]

## Question for You

Q) For a Right angle Triangle, Tan \theta = 5/12. Find the rest 5 Trigonometric Ratios?

Mention your answer in the comment below.

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