# Write The Given Expression in Algebraic Form

1. Aug 27, 2009

### Centurion1

1. The problem statement, all variables and given/known data
Write the Given Expression in algebraic Form
sin(arctan x 5/x)

2. Relevant equations

3. The attempt at a solution
Do you just simplify the arcy=tan to fit with sin? So does it just become a simple simplification problem? Oh and does algebraic form mean without the sin and arctan?

2. Aug 27, 2009

### Elucidus

The argument of the arctangent function is not clear. Is there an operator missing or is it really (x times 5/x)?

Regardless, these sorts of questions can be handled with roughly the same approach. Consider $y=\cos(\arcsin u)$. If we let t = arcsin u, then we have y = cos t and sint t = u. Since u = opp/hyp we can draw a right triangle with acute interior angle labeled t where opp/hyp = u/1 and put u on the opposing side from t and 1 adjacent to it.

Calculating the hypotenuse we get $\sqrt{(1+u^2)}$ by using the Pythagorean Theorem. Using this triangle it is not hard to find y = cos t.

--Elucidus

3. Aug 29, 2009

### Centurion1

the x means multiplication

4. Aug 29, 2009

### Elucidus

Your original question concerned the function sin(arctan x 5/x). Arctan is a function name and cannot be "multiplied" or do you mean arctan of 5/x?

--Elucidus

5. Aug 30, 2009

### Centurion1

yes sorry that is what i meant. I realize you cannot multiply that