Question

Find sin y if CSC Y= -square 6/2.

A. sin y = -1/√6
B. sin y = -√6/2
C. sin y = √6/2
D. sin y = 1/√6

Answer 1

The value of sin y when CSC Y = -sqrt(6)/2 is sqrt(6)/2.

Step-by-step explanation:

To find sin y when CSC Y = -sqrt(6)/2, we need to find the value of y in the unit circle that corresponds to CSC Y = -sqrt(6)/2. The reciprocal of CSC Y is sin y, so we need to find sin y when CSC Y = 2/(-sqrt(6)).

We can start by finding the value of y in the unit circle that corresponds to CSC Y = 2/(-sqrt(6)). Since CSC Y is negative, y must be in either the second or third quadrant. In the second quadrant, the sin function is positive, so we can write sin y = sqrt(1 - cos^2 y). If CSC Y = 2/(-sqrt(6)), then sin y = sqrt(1 - (1/Y^2)) = sqrt(1 - (1/((-sqrt(6)/2))^2)) = sqrt(1 - 4/6) = sqrt(1/6) = sqrt(6)/sqrt(36) = sqrt(6)/6. Thus, the correct answer is C. sin y = sqrt(6)/2.