Write The Given Expression in Algebraic Form

[Centurion1]

Homework Statement

Write the Given Expression in algebraic Form
sin(arctan x 5/x)

Homework Equations

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?

 

[Elucidus]

Homework Statement

Write the Given Expression in algebraic Form
sin(arctan x 5/x)

Homework Equations

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?

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.

Your exercise is handled similarly.

--Elucidus

 

[Centurion1]

the x means multiplication

 

[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

 

[Centurion1]

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