Tuesday, 4 June 2013

TRIGNOMETRY, PURPOSE AND SIGNIFICANCE OF SIN,COS, TAN ETC ALONG WITH APPLICATION AND EXAMPLES

TRIGONOMETRY
PURPOSE OF SIN,COS,TAN ETC ALONG WITH EXAMPLES AND ANALOGIES.

THE PURPOSE OF SIN

|||| Sin is a measure of how much perpendicular two objects or forces are.

|||| Sin appears in Mathematics whenever two objects produce maximum force or maximum effect when acting at 90 degree.

|||| For example, a ball hitting a wall will  produce maximum impact at 90 degrees. Hence Sin(90)=maximum=1.

|||| Similarly, a ball hitting a wall at 30 degree if measured, produces half the impact, i.e only half the force of the ball is transferred to the wall. Hence sin(30)=1/2.

|||| At 0 degree, the ball goes parallel to the plane of the wall, and so, there is no impact.

THE PURPOSE OF COS
|||| Cos is a measure of how much parallel two objects are. 

|||| Cos comes into mathematics whenever two  objects or forces produce maximum results when they work parallel to each other.

|||| Hence at 0 degrees, Cos(0)=maximum=1.

|||| For example, when you row a boat parallel to the flow of the river, the resultant force is the maximum.

|||| If you dare to flow  any less parallel (i.e at any angle other than 0 degrees), your boat wont go ahead with the same velocity.

|||| It will now move only with a fraction of the velocity that was there previously.

||||  This fraction is what you usually get as the fractions involving cos. For example, if your boat is moving at 60 degrees with respect to the flow of the river, the river reduces the velocity of your boat to Cos(60) = 1/2 =half of its velocity than what it was at 0 degree.

|||| At 90 degrees, your rowing and the rivers flow are completely out of alignment. You both are not even 1% working in alignment with each other.

|||| Hence Cos (90 ) =0 = 0



The above was an except from a book called as 'VISUALIZING MATHS'. It's available on Amazon.com at the link below OR via PAYPAL at the link-button below.

3 comments:

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    1. +vaidevi
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