Asked by girly girl
Explain why sin^-1[sin(3pi/4)] does not = 3pi/4 when y=sin(x) and y=sin^-1(x) are inverses.
Any help on this question is greatly appreciated. Thank you!
Any help on this question is greatly appreciated. Thank you!
Answers
Answered by
bobpursley
sin(3PI/4) is a specific number. The inverse of that number can track to several angles, all of which have the same value of sine.
Example; arcsin(sin30deg).
well sin 30 deg=.5
but arcsin(.5) can be 30 deg, 150 deg, and so on...
Example; arcsin(sin30deg).
well sin 30 deg=.5
but arcsin(.5) can be 30 deg, 150 deg, and so on...
Answered by
Damon
well sin 3 pi/4 = +1/sqrt 2 = +sqrt 2/ 2 in quadrant 2
BUT
sin pi/4 = +sqrt2 / 2 in quadrant 1
sin(3pi/4) = sin(pi/4)
sin^-1 (sqrt2 /2) = 45 degrees and sin^-1(sqrt2/2) = 135 degrees
so for example
sin^-1 (sin3pi/4) = pi/4
BUT
sin pi/4 = +sqrt2 / 2 in quadrant 1
sin(3pi/4) = sin(pi/4)
sin^-1 (sqrt2 /2) = 45 degrees and sin^-1(sqrt2/2) = 135 degrees
so for example
sin^-1 (sin3pi/4) = pi/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.