How to find the inverse of a trig function?

Science & Mathematics by Anonymous 2018-06-28 02:33:44

Social Science

2 answers

Hello, I am looking for the inverse of 3 Sin(2x+7). The answer for the inverse is sin^-1 (x/3) - 7/12. I would greatly appreciate if someone would tell me steps in order to get to the answer. Thanks.

Anonymous

y = 3 sin (2x + 7) sin (2x + 7) = y/3 2x + 7 = sin^(-1) [ y/3 ] 2x = sin^(-1) [ y/3 ] - 7 x = (1/2) sin^(-1) [ y/3 ] - 7/2 f^(-1)(y) = (1/2) sin^(-1) [ y/3 ] - 7/2 f^(-1)(x) = (1/2) sin^(-1) [ x/3 ] - 7/2
Anonymous

y = 3 sin(2x+7) y/3 = sin(2x+7) sin^-1(y/3) + 2nπ = 2x+7 where n is any integer sin^-1(y/3) + 2nπ - 7 = 2x [sin^-1(y/3) + 2nπ - 7]/2 = x The inverse is y = [sin^-1(y/3) + 2nπ - 7]/2 The inverse is not a function as there are multiple values for each input