Question

Given that cos 0 = x/6

Which expression represents 0 in terms of X?
Arcsin (x/6)
Cos(x/6)
Arccos (x/6)
Sin (x/6)

Answer 1

The expression that represents
`\theta` is

`\theta=arccos((x)/(6))`

Explanation:

The trigonometric equation given to us is

`cos(\theta)=(x)/(6)`

We take the cosine inverse of both sides to obtain,

`arccos(cos(\theta))=arccos((x)/(6))`

Recall that, the composition of a function of x and its inverse produces x.

That is
`f(f^(-1)(x))=x` or

`f^(-1)(f(x))=x`

Similarly,
`arccos(cos(\theta))=\theta`

This implies that,

`\theta=arccos((x)/(6))`

The correct answer is C.