How do we know that inverse sine of 1 is pi/2?

Question

anonymous · Answer

Without using a calculator..

unklerhaukus · Answer

A 'triangle', with is opposite side and hypotenuse of equal length, must have two right angles

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anonymous · Answer

ok

unklerhaukus · Answer

sine angle = opposite  / hypotenuse 
sine angle = 1   -->   opp = hypo
 angle = 90 degrees = pi/2 radians

anonymous · Answer

How did you receive the third step? How the angle equals 90 degrees?

unklerhaukus · Answer

from the picture

anonymous · Answer

wait so are you saying the only way the sine of the angle can equal one is if it is the right angle?

anonymous · Answer

Wouldn't another angle work when the triangle is 45-45-90?

unklerhaukus · Answer

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unklerhaukus · Answer

then sine of the angle:
sin A = opp/hypo   = 1/ sqrt 2

anonymous · Answer

Okay, I see it now! Thanks :)

unklerhaukus · Answer

as the opposite side gets bigger, and approaches the length of the hypotenuse, that angle A approaches 90 degrees

unklerhaukus · Answer

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unklerhaukus · Answer

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