Find the exact value of csc(-1740)degrees

let's recall that negative angles go clockwise, so we have -1740°, how many revolutions is that?  1740 - 360 - 360 - 360 - 360 = 300, meaning, that 360 + 360 + 360 + 360 + 300 = 1740.

So, if we move clockwise and go around 4 times over, and then land on -300°, we'll be landing on the 1st Quadrant as you see in the picture below.

Step-by-step explanation:

Consider

We know that angle lies in fourth quadrant and is negative in the fourth quadrant .

So,

We can write as

Therefore,

Here, lies in fourth quadrant in which cosec function is negative, so

yes

step-by-step explanation:

yes