+9673 40.2443sin (0.0729x + 4.6878) + 40.3295 = 90
40.2443sin (0.0729x + 4.6878) = 49.6705
sin (0.0729x + 4.6878) = 49.6705/40.2443 (= 1.234224474024893)
Because the function sine will only give out answers between -1 and 1
Therefore sin (0.0729x + 4.6878) = 1.234224474024893 is impossible
So there are no solutions to this equation
Solve for x:
90 = 40.3295+40.2443 sin(0.0729 x+4.6878)
40.3295+40.2443 sin(0.0729 x+4.6878) = 80659/2000+(402443 sin((729 x)/10000+23439/5000))/10000:
90 = 80659/2000+(402443 sin((729 x)/10000+23439/5000))/10000
90 = 80659/2000+(402443 sin((729 x)/10000+23439/5000))/10000 is equivalent to 80659/2000+(402443 sin((729 x)/10000+23439/5000))/10000 = 90:
80659/2000+(402443 sin((729 x)/10000+23439/5000))/10000 = 90
Subtract 80659/2000 from both sides:
(402443 sin((729 x)/10000+23439/5000))/10000 = 99341/2000
Multiply both sides by 10000/402443:
sin((729 x)/10000+23439/5000) = 496705/402443
Take the inverse sine of both sides:
(729 x)/10000+23439/5000 = pi-sin^(-1)(496705/402443)+2 pi n_1 for n_1 element Z
or (729 x)/10000+23439/5000 = sin^(-1)(496705/402443)+2 pi n_2 for n_2 element Z
Subtract 23439/5000 from both sides:
(729 x)/10000 = -23439/5000+pi-sin^(-1)(496705/402443)+2 pi n_1 for n_1 element Z
or (729 x)/10000+23439/5000 = sin^(-1)(496705/402443)+2 pi n_2 for n_2 element Z
Multiply both sides by 10000/729:
x = -15626/243+(10000 pi)/729-10000/729 sin^(-1)(496705/402443)+(20000 pi n_1)/729 for n_1 element Z
or (729 x)/10000+23439/5000 = sin^(-1)(496705/402443)+2 pi n_2 for n_2 element Z
Subtract 23439/5000 from both sides:
x = -15626/243+(10000 pi)/729-10000/729 sin^(-1)(496705/402443)+(20000 pi n_1)/729 for n_1 element Z
or (729 x)/10000 = -23439/5000+sin^(-1)(496705/402443)+2 pi n_2 for n_2 element Z
Multiply both sides by 10000/729:
Answer: | x = -15626/243+(10000 pi)/729-10000/729 sin^(-1)(496705/402443)+(20000 pi n_1)/729 for n_1 element Z
or x = -15626/243+10000/729 sin^(-1)(496705/402443)+(20000 pi n_2)/729 for n_2 element Z
