Question

find the exact value of the given expression sin(5pi/3-5pi/4)

Answer 1

sin(u-v) = sin(u)cos(v)-cos(u)sin(v)
u = 5pi/3
v = 5pi/4

Answer 2

i did that and got radical 6 -radical 2/4

Answer 3

Hmm... I got
\[\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\]

Answer 4

but that was marked wrong?

Answer 5

I don't know then. Unless I'm totally forgetting the unit circle, that's right.

Answer 6

okay what about sin(arcsinx+arccosx) how do i simplify that?

Answer 7

sin(u+v) = sin(u)cos(v)+cos(u)sin(v)
sin(asin(x)+acos(x))
sin(asin(x))cos(acos(x)) + cos(asin(x))sin(acos(x))
x² + (1 - x²)
1

sin(acos(x)) = cos(asin(x)) = sqrt(1-x²)

Answer 8

So it simplifies to 1