Trigonometric equations with sin and cot

[dbg11]

Homework Statement

find the value(s): cot(2sin^(-1) 2/7)

The Attempt at a Solution

I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came out to 4 sqrt(3). From the x value I was able to find the cosine. Since cotangeant is cosine/ sine I solved for that to get my exact value but it did not come out to the correct answer.
I think it had something to do with the (2 sin) in the equation. I am not sure exactly what to do when an equation gives me a number times sine.

 

[Mathoholic!]

$\frac{1}{tan(\frac{2}{sin(2/7)})}$ ?

 

[Mark44]

Homework Statement

find the value(s): cot(2sin^(-1) 2/7)

The Attempt at a Solution

I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came out to 4 sqrt(3).

I get 3√5, not 4√3.

From the x value I was able to find the cosine. Since cotangeant is cosine/ sine I solved for that to get my exact value but it did not come out to the correct answer.
I think it had something to do with the (2 sin) in the equation. I am not sure exactly what to do when an equation gives me a number times sine.