Simplifying sin(arctan(x/4))

[student1405]

[Mentor's note: This thread was originally posted in a non-homework forum, so it doesn't follow the homework template.]

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Sin(arctan(x/4))= ?

Been over 2 years since I've done some math, a little help please?

 

[Bacle2]

Set up a right triangle with sides x and 4, so that the tangent of one of the angles is x/4, i.e., tanθ=x/4. Then θ=tan^{-1}(x/4) . From the drawing, figure out the value of sinθ.

 

[SteamKing]

It might help you if you draw a triangle and split the expression above into component parts.

First, how would you triangle look if you were to show what arctan(x/4) meant?

 

[student1405]

Ok I:

Drew a triangle in quadrant 1 to represent x/4 and labeled the angle A for random sake
then used Pythagorean theorem to find the hyp
after solving for sign and rationalizing I came up with:

SinA= (x(√(x^2)+16)/((x^2)+16) ------ √ ending after the first 16
sound right?

 

[ehild]

Yes, $\sin(A)=x\frac{\sqrt{x^2+16}}{x^2+16}$.

ehild