Find the value of the trigonometric function cosec (–1410°)

Sure, let's solve this step by step:

Step 1: Convert the negative angle to a positive angle. Since the trigonometric functions are periodic with a period of 360°, we can add 360° to the angle until we get a positive angle.

-1410° + 4*360° = 60°

So, cosec (–1410°) is equivalent to cosec (60°).

Step 2: Find the value of cosec (60°). The cosecant is the reciprocal of the sine function. So, we need to find the value of sin (60°) first.

sin (60°) = √3/2

Therefore, cosec (60°) = 2/√3 = 2√3/3

So, the value of cosec (–1410°) is 2√3/3.