I WOULD LIKE AN ACRUAL EXPLANATION, I NEED TO UNDERSTAND THIS, THANK YOU
csc^-1 4.25 to degrees​

9514 1404 393

  13.609°

Step-by-step explanation:

The csc^-1 function is the arccosecant function. It gives the angle whose cosecant is given. If we let A represent that angle, your statement is ...

  A = csc^-1(4.25)

It is used to solve the relation ...

  4.25 = csc(A)

__

Some calculators can give you the value directly (see attached). Most cannot. In any event, you need to make sure the angle mode for the calculator is set to degrees.

When your calculator does not have the csc^-1 function, you can make use of the trig identity ...

  csc(x) = 1/sin(x)

In the above equation, this becomes ...

  4.25 = 1/sin(A)

  sin(A) = 1/4.25 . . . . . solve for sin(A)

All scientific and graphing calculators will have the inverse sine (arcsine) function.

  A = sin^-1(1/4.25)

  A ≈ 13.609° . . . . . . . calculator mode in Degrees

_____

Additional comment

For inverse functions, especially inverse trig functions, I find it useful to read them as ...

  csc^-1(x)   ⇒   "the angle whose cosecant is x"

  sin^-1(x)   ⇒   "the angle whose sine is x"

This reminds me that the value it gives is an angle (degrees or radians), and the argument it takes is a pure number (one with no units).

about 168 miles

step-by-step explanation: