Question

Question

Given that cot(0)= -1/2
and O is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.
Provide your answer below:

Answer 1

sin(O) = 2/sqrt(5) or 2sqrt(1/5)

Explanation:

using 1+cot^2(x) = csc^2(x)

we have, taking reciprocal on both sides,

sin(x) = 1/sqrt(1+cot^2(x)

= 1/sqrt(1+(-1/2)^2)

= 1/sqrt(5/4)

= 2/sqrt(5) or 2sqrt(1/5)

Since angle x is in the second quadrant, sin(x) is positive.