Question

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

Answer 1

Without using a calculator..

Answer 2

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

Answer 3

ok

Answer 4

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

Answer 5

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

Answer 6

from the picture

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Okay, I see it now! Thanks :)

Answer 11

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