Find the value of cosec(-570°).


Solution:

To find cosec(-570°) = ?

= cosec(-570°)

= cosec(-540°- 30°)

= cosec(-3*180° - 30°)
 
= cosec(-3π - 30°)

= -cosec 30°

= -(2)

= -2

Hence, the value of cosec(-570°) is (-2).


Explanation:



Here, to find the value of cosec at -570° angle we need to make sure that we know the CAST FORMULA. We might need to use formula of cosec at (90-x) or (90+x) or (180+x) or (360-x) and so on.

Here are the identities we have used:

1. cosec A = 1/sinA
2. cosec30° = 1/sin30°
3. cosec30° = 2

These are some of the commonly asked questions from values of compound angles of Trigonometry. 

You should always try to break the given value in the form of either (π+A) or (π-A). 

And, we know that the value of π is equal to 180°.

Then, we can use the cast formulae and find the answers. 


Here we have evaluated the value of cosec (-1485°) which is a negative angle but has some relation with the angles that can be obtained from the value table of Trigonometry. Since this is a compound angle, we have to deal with two angles, one being the known angle such as 0°,30°,45°,60° or 90° and other angle being the multiple or sub-multiple of 180° (written as π). 



cosec (-570°)



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