Find the exact value of the following expression csc pi6 squ

Find the exact value of the following expression. csc [pi/6] squareroot 2 1/2 2 2 squareroot 3/3 sec (150 degree) 2 squareroot 3/3 squareroot 2 - squareroot 2 - 2 squareroot 3/3 Find the exact value of the real number y. y = arctan(squareroot 3) pi/3 pi/6 3 pi/4 1 pi/4 y = arccos [cos pi/2] pi/2 pi/3 pi 0

Solution

12) Option C)

csc(pi/6) = 1/sin(pi/6) = 1/(1/2) = 2

13) Option D)

sec(150 deg)=1/cos(150 deg)
Now cos(150 deg)=cos(90 deg+60 deg)
=cos(90 deg)cos(60 deg)-sin(90deg)sin(60 deg)
= -sin(60 deg) since cos(90 deg)=0 and sin(90 deg)=1
= -sqrt(3)/2.

So sec(150 deg) = -2/sqrt(3)

14) option A)

y = arctan(sqrt(3)) = arctan(tan pi/3) = pi/3

15) Option A)

y = arccos(cos pi/2) = pi/2