Find the value of cosec (–1410º)

Sure, let's solve this step by step.

Step 1: Convert the angle to a value between 0 and 360 degrees because the trigonometric functions repeat every 360 degrees. We can do this by adding or subtracting 360 degrees until we get a value in this range.

-1410 + 4*360 = -1410 + 1440 = 30 degrees

So, cosec (–1410º) is equivalent to cosec (30º).

Step 2: Now, we need to find the value of cosec (30º). The cosecant is the reciprocal of the sine function. So, we need to find the value of sin (30º) first.

sin (30º) = 1/2

Step 3: Now, find the reciprocal of sin (30º) to get cosec (30º).

cosec (30º) = 1 / sin (30º) = 1 / (1/2) = 2

So, the value of cosec (–1410º) is 2.