Question

Given sin(-t) = 2/3, find csc (t).

Answer 1

`\displaystyle \csc(t)=-(3)/(2)`

Explanation:

`\displaystyle \sin(-t)=(2)/(3)\\\\\sin(t)=-(2)/(3)\\ \\(1)/(\sin(t))=(1)/(-(2)/(3))\\\\\\\csc(t)=-(3)/(2)`

The second step can be done because sin(-t) is an odd function.

Answer 2

csc(t) = -3/2

Explanation:

Given sin(-t) = 2/3, we can find the value of csc(t) as follows:

sin(-t) = 2/3

sin(t) = -2/3 (since the sine function is an odd function)

Since csc(t) = 1/sin(t), we have:

csc(t) = 1/sin(t) = 1/(-2/3) = -3/2