Question

Find the exact value of each expression, if it exists:

the -1 are representing the inverse functions!

(a) sin -1 (-√2/2)

(b) cos−1 (−1)

(c) sin( 􏰀sin−1 (π)􏰁)

(d) cos−1􏰀(cos􏰀(−4π􏰁􏰁/ 3))

(e) tan−1 (tan(0.6))

(f) cos−1( 􏰀cos􏰀13π􏰁􏰁/12))

(g) tan( 􏰀sin−1 􏰀 (8 􏰁􏰁 /17))

(h) cot (􏰀cos−1 􏰀( 5 􏰁􏰁/13))



these are what i have. I'm looking to make sure i have done them correctly. If i haven't if you could show me the work to the ones i got wrong that would be great!

a. -π/4
b. π
c. undefined because domain [-1,1]
d. -4π/3
e. .6
f. undefined because domain [0, π]
g. 8/15
h. 5/12

Answer 1

d: the arccos has principal vales from 0 to π.

cos(-4π/3) = -1/2
cos^-1(-1/2) = 2π/3

f:
cos(13π/12) = -cos(π/12) = -x
arccos(-x) = π-arccos(x) = 11π/12


The others look good. Be careful with the principal values stuff.