first let' s do
cos 5π/4 or cos 225°
Make a sketch of your right - angled isosceles triangle in quadrant III
we know cos 225 = -1/√2
so
cos^-1 [cos (5π/4) }
= cos^-1 [ -1/√2)
= 5π/4
or
= 3π/4 --- in the 2nd quadrant, by CAST the cosine is negative in II or III
try this on your calculator:
(set to radians)
enter:
cos
(5xπ÷4) =
--- you should see : -.707...
now press:
2ndF cos
=
--- you should see 2.356... which is the value of 3π/4
(your calculator is programmed to always give you the closest angle to zero, 3π/4 (135°) is closer to 0 than 5π/4 (225°) )
in general , for any mathematical operator 'job'
job^-1 (job (k) ) = k
Explain
cos^-1 [cos 5pi/4]
also tell it can be defined or not.
1 answer