Question

Find a numerical value of one trigonometric function of x if sinxcotx=1/3

Answer 1

sin x cotx = sin x * cos x / sin x = cos x

so cos x = 1/3

Answer 2

A numerical value of one trigonometric function of x, for the given function would be
`cos(x)=(1)/(3)`

Explanation:

We know that there are many trigonometric functions, that can be expressed as functions of x, for example:

`sin(x)`

`cos(x)`

`tan(x)`

`cot(x)`

`csc(x)`

So, the problem is aking us for one trigonometric function of x, but gives us a product of functions of x, instead of one function of x. We note then, that

`cot(x)=(cos(x))/(sin(x))`

Therefore, we calculate from the given function

`sin(x)*(cos(x))/(sin(x))=cos(x)=(1)/(3)`

wich is our answer, furthermore, we could calculate the value of x for this case

`x=cos^-1((1)/(3))\approx70.5`