Question

Find the value of csc 0, if cos 0= - 2/3 ; 180 < 0< 270

Answer 1

D

Explanation:

apply pythagorean theorem to find sin of theta.

`\cos( (2)/(3) ) {}^(2) + \sin(x) {}^(2) = 1`

`((4)/(9)) {}^(2) + \sin(x) {}^(2) = 1`

`\sin(x) {}^(2) = (5)/(9)`

`\sin(x) = ( √(5) )/(3)`

Find the reciprocal to find find csc.

`(3)/( √(5) )`

rationalize the denominator.

`(3)/( √(5) ) * ( √(5) )/( √(5) ) = (3 √(5) )/(5)`

Csc is negative in the 3rd quadrant.

so the answer is

`- (3 √(5) )/(5)`

D is the answer.