# How do you evaluate # csc^-1 (cos(4/7))#?

##### 2 Answers

There is no answer.

#### Explanation:

The

graph{cscx [-10, 10, -5, 5]}

Thus, the inverse function

graph{x=cscy [-10, 10, -1.6, 1.6]}

In order for **not** between **actually is** between

Thus,

This expression is undefined for

Note however that

#### Explanation:

Note that as real valued functions:

#cos(theta) in [-1, 1]#

#csc(theta) in (-oo, -1] uu [1, oo)#

Note that:

#0 < 4/7 < pi/2#

and hence:

#0 < cos(4/7) < 1#

So there is no real value of

#csc(theta) = cos(4/7)#

**Footnote**

I wonder whether the question should have actually been to find the value of

If so, then we find:

#csc(cos^(-1)(4/7)) = 7/sqrt(33) = (7sqrt(33))/33#