By definition, arcsin(x/2) would be the angle π, so that sinπ = x/2
Using a hunch that perhaps we would deal with one of our standard angles,
I tried x = 0, 1, β2, β3, 2 , (which would be sides in our standard 45-45-90 and 30-60-90 triangles
for x = 0 ,
(arcsin(0)+arccos(0))/arctan(0) = (0 + 1)/0 β 3/2
for x= 1
(arcsin(1/2)+arccos(1/2)/arctan(2) = (30 + 60)/63.43.. β 3/2
x = β2
(arcsin(β2/2)+arccos(β2/2)/arctan(β2) = (45+45)/54.7... β 3/2
x = β3
(arcsin(β3/2)+arccos(β3/2)/arctan(β3) = (60 + 30)/60 = 90/60 = 3/2
Well, how is that for a "lucky" guess
At the moment, I can't think of a formal way to solve this.
(arcsin(x/2)+arccos(x/2))/arctan(x) = 3/2, solve for x if x >0. Thanks.
1 answer