Question

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

Answer 1

Answer:

D

Step-by-step explanation:

apply pythagorean theorem to find sin of theta.

$\cos( \frac{2}{3} ) {}^{2} + \sin(x) {}^{2} = 1$

$(\frac{4}{9}) {}^{2} + \sin(x) {}^{2} = 1$

$\sin(x) {}^{2} = \frac{5}{9}$

$\sin(x) = \frac{ \sqrt{5} }{3}$

Find the reciprocal to find find csc.

$\frac{3}{ \sqrt{5} }$

rationalize the denominator.

$\frac{3}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{3 \sqrt{5} }{5}$

Csc is negative in the 3rd quadrant.

so the answer is

$- \frac{3 \sqrt{5} }{5}$

D is the answer.