ok, so i have an exam tomorrow, and i am required to know how to solve inverse trig functions without a calculator. i wasnt able to comprehend the way my instructor taught it and have absolutely no clue on how to approach the problem-solving method. an example of one of these problems would be sin^-1(1/2). as well as sin^-1[sin(-pi/8)]. my instructor did not teach us using the unit circle method therefore i do not know the corresponding relationships. Thank you very much to those that legitimately try to help!
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go to 'wikipedia.org' , type in inverse trig functions , read
Θ = sin^-1 ( 1 / 2 ) means sin Θ = 1 / 2 and you should know that Θ = π / 6
µ = sin^-1 [ sin ( - π / 8 ) ] means sin µ = sin ( - π / 8) and µ = -π / 8
however note that sin ( - π / 8 ) = sin ( 9π / 8 ) but sin^-1 [ sin ( 9π / 8 ) ] is not 9π / 8 ;
rather it is - π / 8...has to do with domain and ranges of the inverse functions
Θ = sin^-1 ( 1 / 2 ) means sin Θ = 1 / 2 and you should know that Θ = π / 6
µ = sin^-1 [ sin ( - π / 8 ) ] means sin µ = sin ( - π / 8) and µ = -π / 8
however note that sin ( - π / 8 ) = sin ( 9π / 8 ) but sin^-1 [ sin ( 9π / 8 ) ] is not 9π / 8 ;
rather it is - π / 8...has to do with domain and ranges of the inverse functions