find the exact value of sin(cos(-13/5)) explain please! i have the answer from the back of the book, which is 4/5 , but i dont know how to get there. Thanks!!

Question

mathstudent55 · Answer

Is it cos(13/5) or arccos(-13/5) ?

anonymous · Answer

just cos

anonymous · Answer

sin(cos(-13/5)

mathstudent55 · Answer

It's not this?

$\sin (\cos^{-1} \left(-\dfrac{13}{5} \right))$

anonymous · Answer

no

phi · Answer

how about
$$ \sin \left(\cos^{-1}\left(\frac{3}{5}\right) \right) $$

anonymous · Answer

$$\sin(\cos \frac{ -13 }{ 5 }$$

anonymous · Answer

can i change it to that... pi?

mathstudent55 · Answer

Is there an "exponent" of -1 on the cosine?

phi · Answer

the little -1 next to the cos means  inverse cosine
it means find the angle whose cosine is 3/5

phi · Answer

it is "special terminology"   
because it is confusing this same problem might also be written as
$$ \sin \left( acos\left( \frac{3}{5}\right) \right) $$

phi · Answer

or even
$$ \sin \left( \arccos\left( \frac{3}{5}\right) \right) $$

anonymous · Answer

ok that makes more sense.. hold on while i try to figure it out

anonymous · Answer

so would the 3 be the adjacent side and 5 be the hyp.

phi · Answer

yes.  use pythagoras to find the other leg (the opposite side)
the sin of the angle is opp/hyp

anonymous · Answer

AWESOM!!!!! thank you so much

anonymous · Answer

can i ask u another question

phi · Answer

please make it a new post.