SOLUTION: Write the trigonometric expression sin (cot-1 u) as an algebraic expression in u.

Question 820355: Write the trigonometric expression sin (cot-1 u) as an algebraic expression in u.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
is a reference to an angle. Specifically it is an angle whose cot ratio is "u" or

It will probably help if you have a drawing:

Draw a right triangle.
Choose one of the acute angles and label it A. This will be the angle represented by .
We want cot(A) to be . Since cot is adjacent/opposite, label the side adjacent to A as "u" and the side opposite to A as "1". This makes cot(A) = u.

Now we want to find the sin(A). Since sin is opposite/hypotenuse and since we do not yet have the the hypotenuse, we must find the hypotenuse next. Using the Pythagorean Theorem we get:
(where "h" stands for the hypotenuse)
Simplifying:

Square root of each side. (And since the hypotenuse is never negative, we will use only the positive square root (and not use a + as usual).

Now we can find the sin (opposite/hypotenuse):

This may be an acceptable answer.

But it does have a square root in the denominator. So we may want to rationalize it:

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