Why The highest Value of Sine is 1
Describe please
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because the highest magnitude of angle is 90 nd sin (angle)= opposite side of triangle / hypotenuse nd in case of angle 90 sin 90 = hypotenuse/ hypotenuse nd it is 1
kvnmurty:
using a circle, for definition of sine and cosine ratios will be better.
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★ TRIGONOMETRIC RESOLUTIONS ★
Trigonometry originated from circles , in the ancient times , classical models of geometric figures were evolving on a wide scale ,
the most significant figure deviced was a circle , planetary motion's circular orbiting concepts and ellipsoids , and many more subsequently ,
When we consider Sinθ , it's actually angle described between Perpendicular and hypotenuse , in a unit circle , a unit circle is stated as having 1 unit standard radius ,
Sinθ is operated as a whole numerical value at the end up result , what actually happens is , for describing any angle , we should must have two lines intersecting at a common point , so that we can measure the angle , Sine of any angle is obtained by the same concept , we state it as P/H , perpendicular divided by hypotenuse ,
ratio can be maximum of 1 , means , P = H [ line segment is rotated 90° anti clockwise ]
It'll not form any triangle , but , we'll be left with two successful line segments interested at a common point , from where we can obtain the value of Sinθ
I've presented 2 proofs above ,
first one is trivial proof , another is a geometrical mathematical generality ,
Hence , we concluded that , Sinθ has maximum value of 1
The attachment above has the same unit circle with every TRIGONOMETRIC ANGLES available to us , the side lengths are itself the ratio called Sine , Cosine , ... and so on
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
Trigonometry originated from circles , in the ancient times , classical models of geometric figures were evolving on a wide scale ,
the most significant figure deviced was a circle , planetary motion's circular orbiting concepts and ellipsoids , and many more subsequently ,
When we consider Sinθ , it's actually angle described between Perpendicular and hypotenuse , in a unit circle , a unit circle is stated as having 1 unit standard radius ,
Sinθ is operated as a whole numerical value at the end up result , what actually happens is , for describing any angle , we should must have two lines intersecting at a common point , so that we can measure the angle , Sine of any angle is obtained by the same concept , we state it as P/H , perpendicular divided by hypotenuse ,
ratio can be maximum of 1 , means , P = H [ line segment is rotated 90° anti clockwise ]
It'll not form any triangle , but , we'll be left with two successful line segments interested at a common point , from where we can obtain the value of Sinθ
I've presented 2 proofs above ,
first one is trivial proof , another is a geometrical mathematical generality ,
Hence , we concluded that , Sinθ has maximum value of 1
The attachment above has the same unit circle with every TRIGONOMETRIC ANGLES available to us , the side lengths are itself the ratio called Sine , Cosine , ... and so on
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
Attachments:
THANKS SIR !
request that the language in the explanation be simpler .. so that it is more easily understood by 8th 9th class students too. the language used in the answer is like that written in research papers.
I'll take care of this point sir :)
just this diagram is enough to understand... beyond that other explanation is tough
I got it sir , I'll follow your precious words
** Quality Explanation ** You have taken a lot of time and given a lot of effort. thanks. great it is.
My pleasure sir ^_^
In right triangle ABC, AC is the Hypotenuse. B=90 deg. Sin A = BC/AC = sqrt {[AC^2 - AB^2] / AC} = sqrt [1 - (AB/AC)^2 ] = 1 as minimum value of AB/AC = 0 when AB=0.
Is that explanation not enough?
perfect sir ^_^
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