 Computing Trigonometric Ratios

In certain places, Vedic Mathematics talks about trigonometrical triplets, which became famous as Pythagorean triplets much later. So was the outcome of Pythagorean theorem known to Indians?

Without going into that discussion, let us see how this concept of triplets can be extremely effective in solving many types of trigonometric problems.

Let us define a triplet in a triangle as a (i.e. base), b (i.e. perpendicular) , c (hypotenuse). Here, ‘a’ and ‘b’ are the measures of the two sides followed by the hypotenuse (‘c’) at the end.

The relationship c2 = a2 + b2 holds true in this case.

Thus if any two values of the triplet are given, we can compute the 3rd value and build the complete triplet. Let us see some examples of how to build and use the triplet.

Case 1: suppose that a = 3 and b = 4. Let us see how to build triplet.

Given partial triplet is 3, 4, ______

Therefore the last value will be = √ (32 + 42) = 5. Hence the completed triplet is 3, 4, 5.

Case 2: If we’re given an incomplete triplet as 12, ___, 13. The missing value will be √ (132 – 122) = 5. Hence, the completed triplet would be 12, 5, 13.

Once the triplet is built, all the six trigonometric ratios can be read off easily without any further computation or use of any formulae.

Computing Trigonometric Ratios

If tan A = 4/3, find Cosec A.

Normally to find this we will use the formula –

Cosec2 A = 1 + Cot2 A

as, tan A = 4/3, cot A = ¾

On substituting this value in the given formula, we get

Cosec2 A = 1 + 9/16

=  25/16

and cosec A = 5/4, sin A = ⅘

Let us now see how to use triplets method of Vedic Maths to find cosec A and avoid various steps shown above.

The incomplete triplet in this example is

3, 4, ___

tan A = 4/3 = p / b

The complete triplet would be 3, 4, 5.

Hence, cosec A = h / p = 3/5

Isn’t this simply amazing? There’s more to come. We can also calculate double-angle and half-angle using similar method which we will discuss in a future post based on your interest. Let me know if it helps you! Find Value of Sin and Cos using Fingers

Today I am going to share with you a special memory trick for trigonometry, mailed to me by Debasis Basak – a young Class IX follower of QuickerMaths.com

By this method we can find out Sines and Cosines of different angles. It just requires your left hand. Let’s understand this trick step by step –

Step 1:-
First mark the angles of 0, 30, 45, 60, and 90 on little, ring, middle and pointer finger and thumb of your left hand.

Step 2:-
On the palm of your left hand write the equation √x /2 Step 3:-
Suppose, you want to find Cos30.

Fold the finger representing 30. i.e. ring finger of your left hand palm.  Count the numbers of fingers on the left of the ring finger. So since there are 3 fingers, x=3; put the value in the equation given in step 2

Step 4:-
Hence,
Cos30 = √3/2

Finding Sine of the same angle is just a simple step away. Of the same left hand, if we count the fingers to the right of the folded finger, we will get value of sine.

Sin30 = √1 /2 = 1/2

Let’s take another example, sin60

60 is represented by pointer finger and there are 3 fingers to the right of this folded finger.

Hence, sin60 = √3/2

I appreciate the efforts of Debasis in sharing this trick with all of us. In case you want to share some quick calculation trick or technique, mail it to me at vineetpatawari [at] gmail [dot] com.

Memory Tricks for Trigonometry

In the post titled Trigonometry Formula Memorization Trick, I agreed to write about a simple memory trick for memorizing the value of all major angles of different trigonometry ratios like sin30, cos45, tan60, etc. So here you go –

Values of Trigonometric Angles

Let’s start with most commonly used angles of Sin. The angles are 0°, 30° (?/6), 45° (?/4), 60° (?/3), 90° (?/2). For these angles we’ve to make fractions for which we’ve to write 0, 1, 2, 3 and 4 in the numerators and write 4 in the denominator of each fraction. Read More