why cos-1 (√2/2) is 45 degress?

Question

cos^-1 (√2/2) = 45°

Answer 1

you might be tempted to say it's = 45+360n or 315+360n where n= any integer

but

the range of the inverse cosine is restricted to 0 to 180 degrees,

or 0 to pi, by definition, leaving only

45 degrees

= cos^-1(sqr2/2)

= arccos(sqr2/2)

= pi/4 radians

which also

=sin^-1(sqr2/2)

=tan^-1(1)

all other angles whose cosines = sqr2/2 are less than 0 or more than pi

-sin^-1(sqr2/2) and -tan^(-1) also = 45 degrees

range of arcsines and arctangents are from -pi/2 to pi/2