O is an acute angle and sin O is given Use the Pythagorean i

O is an acute angle and sin O is given. Use the Pythagorean identity sin^2O + cos^2O =1 to find cos O. sin O = square root 5/3.

Find the reference angle for the given angle. -11pi/12.

given O is acute angle.

sin^2 O + cos^2 O =1

sinO = sqrt(5/3)

[sqrt(5/3) ]^2 + cos^2 O =1

5/3 +cos^2 O =1

cos^2 O = 1 -5/3

cos^2 O = 2/3

cos O = sqrt(2/3)

given O is an acute angle that means O is less than 90 degree.

2).

reference angle for -11pi/12

-pi +pi/12

pi/12