My calculator displays #sin^(-1)sin 45^o=45^o, sin^(-1)sin 135^o=45^o and sin^(-1)sin 405^o=45^o#.How do you convert this answer from the calculator to the specific starter value? for similar other trigonometric forms?

1 Answer
Oct 15, 2016

The algorithm, of the program that is executed, chooses the

principal value

#x_P in [-pi/2, pi/2]# against the input value x for #sin^(-1)sin x#

Obviously, if you see x as the answer, using f(-1)f(x)=x. do not use the

device. Such an answer is needed, when x radian = x(time), as in the

wave equation, y = sin x, where x = ct.

The general value of x is

#180k+(-1)^k x_P, k =0, +-1, +-2, +-3, ...#

I have used here #pi# radians = #180^o#

For example, the input #x = 405^o#, the answer displayed is

#x_P=45^o#.

#405=180k+(-1)^k 45#, for k =2..

For #cos^(-1)cos x#,

#x= 360k+-x_P#, for suitable k.

For example,for the input #x = 225^o#, the answer displayed is

#x_P=135^o#.

#225=360k+-135#, for k = 1.

for #tan^(-1)tan x#,

it is same as for #sin^(-1)sin x#.