Question

Evaluate the following composition

Answer 1

The value of the given composition is 61/60.

To evaluate csc[
`cos^{-1` (-11/61)], we can start by using the given value of -11/61 to find the angle whose cosine is -11/61. We can use the inverse cosine function to do this:

`cos^-^1` (-11/61) = θ

Next, we can use the cosecant function to find the value of cscθ:

cscθ = 1/sinθ

Since sinθ = √(1 -
`cos^2`θ), we can find sinθ by using the Pythagorean identity:

sinθ = √(1 -
`(-11/61)^2`)

sinθ = √(1 - 121/3721)

sinθ = √(3600/3721)

sinθ = √(3600)/√(3721)

sinθ = 60/61

Therefore, cscθ = 1/(60/61) = 61/60

So, csc[
`cos^-^1` (-11/61)] = 61/60