## Tuesday, 11 June 2013

### Why is Sin(angle) = opposite side/ hypotenuse?

WHY IS SIN (ANGLE) = OPPOSITE SIDE/ HYPOTENUSE.

Example 1
|~~||  Imagine a stick kept between a bulb and a wall.

The Front view of the stick

|~~||  Now the shadow that falls of the stick upon the wall is like the front view of the wall. Now lets say the stick is inclined at 30 degree,  only a small shadow of the stick falls upon the wall.

|~~|| In other words,  the wall presents  the opposite side view of the slanting  stick and thus gives us a measure of how much the length of the stick appears to be reduced due to the inclination.

The Side-view of the stick

|~~|| Now if you look at the stick from the side, you are obviously going to see the actual length of the stick, aren’t  you.

|~~|| No  matter how much the stick is inclined,  does  it  change the side-view?

OPPOSITE SIDE/ HYPOTENUSE = FRONT VIEW/ SIDE-VIEW.

|~~|| The front-view is always influenced by the inclination of the object. So apparently when an object tilts, its front view reduces.

|~~|| The side-view is the actual length of the stick. The side-view is completely unaffected by the slope of the stick.

Thus the formula can be written as

APPARENT LENGTH OF THE STICK AS SEEN FROM FRONT / ACTUAL LENGTH OF THE STICK.

In other words,

Sin = opposite side/ hypotenuse = front view/ side view

Example 1

Just imagine a ladder kept at a slant (inclined).
Now lets visualize the front view and the side view of this ladder.

Now just compare this to our favourite triangle

<-comparing->

COS

Just as sin = opposite side/ hypotenuse.

<-comparing->

DETAILED ANALYSIS (NOT A MUST READ).

What is the detailed significance of this formula?

|||The influence of everything gets divided into two branches, when the force gets inclined at an angle. The two branches are

1] The horizontal component (or Cos (0)).

2] The vertical component (or Sin(0)).

|||| There are other names also for sin and cos, some are as

1] Vertical and horizontal projection

2] Perpendicular and parallel components…..and so on

PRACTICAL APPLICATIONS OF THIS FORMULA.

Example 1

1] Imagine a wall,

|||| Now imagine that the wall is somehow slowly made to incline at 30 degrees. Now if one is standing exactly in front of the wall, his view has to be calculated as,

|||Sin(30) = opposite side/hypotenuse = opposite side / actual  length

|||Therfore 1/2 = opposite side view/ actual length

|||Rearranging, opposite side view = 1/2 actual length .

|||| Thus at 30 inclination, if you stare at any object from the front, you get to see only half of the object.

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THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5\$) AT THE FOLLOWING LINK

AVAILABLE FOR PURCHASE FOR 5\$ (INR 300) HERE (PDF)

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I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it.

Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life.

Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most.
The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.

Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.

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CONTACT
binnoypanicker@gmail.com

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