Find the exact value of the composite function:
sinx ( tanx^-1 (-7/24)) Explain please!

Question

Find the exact value of the composite function:
sinx ( tanx^-1 (-7/24)) Explain please!

anonymous · Answer

|dw:1364178916058:dw|

anonymous · Answer

there is a picture of an angle whose tangent is $\frac{7}{24}$
what you need is the hypotenuse, which you find either by pythagoras 
$$h=\sqrt{7^2+24^2}$$ or else by remembering the $7:24:25$ right triangle

anonymous · Answer

|dw:1364179025424:dw|

anonymous · Answer

now you can see that the sine is $\frac{7}{25}$ except we need to remember that the tangent was negative, and therefore you were in quadrant 4, which means the sine is negative as well

anonymous · Answer

if you have a question let me know, all steps i think are there

anonymous · Answer

Oy well, how do we get to the answer (5√41)/41 o;

anonymous · Answer

hmmm i think you do not
in fact i know you do not

anonymous · Answer

maybe that was for another question

noelgreco · Answer

Tan is <0 in quadrants II and IV.  If the question means explicitly $$\frac{ -7 }{ 24 }$$ and not $$-\frac{ 7 }{ 24 }$$ then we are truly confined to the 4th quadrant.

Otherwise, the solution in II is also correct.

anonymous · Answer

Well, the entire question was (because maybe I set it up wrong):
Given that f(x) = sin x, g(x) = cos x, and h(x) = tan x, find the exact value of the composite function.
f(h^-1 (-(7/24)))

anonymous · Answer

maybe your question was 
$$\sin(\tan^{-1}(\frac{5}{6}))$$

anonymous · Answer

OMG.

anonymous · Answer

no you wrote it right

anonymous · Answer

NO WAIT. I SWITCHED THE QUESTIONS AROUND.

anonymous · Answer

was it 
$$\sin(\tan^{-1}(-\frac{5}{6}))$$

anonymous · Answer

the answer to that one would be $-\frac{5}{\sqrt{41}}$

anonymous · Answer

Wait, no I didn't

anonymous · Answer

That's how it was written

anonymous · Answer

@NoelGreco there is no difference between $-\frac{7}{24}$ and $\frac{-7}{24}$

anonymous · Answer

and the answer was right that you had, I was just looking at the wrong one

anonymous · Answer

Sorryy o;

anonymous · Answer

whew !!

anonymous · Answer

is the method clear?

anonymous · Answer

Yes! (: Thank you very much!

anonymous · Answer

yw

anonymous · Answer

also please note that the domain of $\tan^{-1}(x)$ is $[-\frac{\pi}{2},\frac{\pi}{2}]$ so you are in fact in quadrant 4, and not 2

anonymous · Answer

check that i mean the range, not the domain. the domain is all real numbers

anonymous · Answer

Mhm! (:

anonymous · Answer

the range of arctangent is $[-\frac{\pi}{2},\frac{\pi}{2}]$ so if your answer is negative you are in quadrant 4

anonymous · Answer

Alrighty o: Ty!

anonymous · Answer

yw (again)