We have seen in previous post, that Trigonometric Ratios are w.r.t. angle \theta . Now we will see, how this angle \theta is linked with Trigonometric ratios and how it forms Trigonometric Ratio Table?

Trigonometric Angle Theta
The angle \theta in Trigonometric ratios, to be corelated with angle \theta of a Right angle triangle. Keep this in mind, it will help you in deep understanding of the concept. For a Right angled Triangle, angle \theta range is from 0o to 90o.  [Why \theta can’t exceed 90o? Comment below]


All Trigonometric Ratios, have some value at each angle. This concept can be better understood with a example.

Example: Sin 30o

What actually Sin 30o means. It has 2 components.

1st is Sin, which is Trigonometric Ratio.

2nd is 30o, which is Trigonometric angle \theta of a Right angle Triangle.

For more clarity, lets understand this in respect of a Right angled triangle ABC.

Sin 30 degree

For this Right angled Triangle ABC, we know Sin is AB/AC i.e. ratio of Perpendicular and Hypotenuse.

Means for a right angled triangle ABC with Trigonometric angle \theta as 30o, the ratio of Perpendicular (AB) and Hypotenuse (AC) will be the value of Sin 30o.

Calculate the ratio of Perpendicular (AB) and Hypotenuse (AC) of any random right angle triangle with angle \theta as 30o. It will comes out to be 0.5, which is fixed. You can try this, with any size of triangle, just the Trigonometric angle should be 30o.

Trigonometric ratios experiment

From above animation, we got, sin 30o is 0.5. In similar fashion, we can calculate the value, for all the angles and for all the Trigonometric ratios.

 You can use the calculator to cross check the same.


Till now we understood that, every Trigonometric Ratios have a fixed value, against angle \theta

It will be impossible to remember all the values. So we will limit our self to some specific angles only, which are shown in below TRIGONOMETRIC TABLE.

The Trigonometric table is showing the angles from Left to Right and Trigonometric Ratios from top to bottom. 

Do not try to mug up the Trigonometric table. Try to understand it. In next post, Technique to Remember Trigonometric Table is covered. 

If you want to Know the the derivations of each angle, against each Trigonometric ratio, then click here for FREE Video Lecture on the same.

Experiment @ Home

Draw random Triangles with Trigonometric angle \theta as 30o, 45o & 60o. And measure the Trigonometric ratios using Trigonometric sides and check the validity of the Table.

DO not forget to comment below, with the results.


Q) Find the Side AB & BC in the figure?

Firstly, Identify the Trigonometric sides. Click here to know, how to identify Trigonometric sides.

AC= P = Perpendicular = 5

AB = B = Base = ?

BC = H = Hypotenuse = ?

We have to find Base B & Hypotenuse H. 

Lets proceed with finding Hypotenuse first. The applicable relation between Perpendicular & Hypotenuse is:

Sin 30 degree

Refer Trigonometric Table for value of Sin 30o.

Sin 30 degree

We got Hypotenuse H as 10. i.e side BC is 10. We got 2 sides of Triangle ABC, Lets calculate the 3rd missing side Base B.

Cos 30 degree
Trigonometric Table Cos 30
Cos 30 degree

We got all the 3 sides of the Triangles ABC.

Alternate Approach to the Question:

Once we have got Hypotenuse H, We can also use pythagoras, to find the 3rd missing side Base.   [Comment below with the complete answer]

Question for you:

Q) Find length of all sides and all angles of Right angle triangle, given below? Area of the triangle is 50 \sqrt { 3 }.

Trigonometric Ratio Question

[Paste your answer in the comment section]

[Ask for Hint in the Comment section]

Watch the Complete Video of this Lecture with help of Animation Tool.

(Visualize the concept, in totally different way)

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