Find the exact value by using a half-angle identity.

sin (7pi/8)

Question

Find the exact value by using a half-angle identity.

sin (7pi/8)

anonymous · Answer

i need answers in radicals:)

aravindg · Answer

express 7pi/8 as sum  or difference of two angles

anonymous · Answer

can you explain further....?

e.cociuba · Answer

sin(7pi/8) = +_ ( sqrt( 1- cos(14pu/8)/2) 

= sqrt ( (1- cos7pi/4)/2 ) 

= sqrt ( 1-sqrt(3)/2 )/2 ) 

=sqrt (2 -sqrt(3))/2

It depends on the angel and assumption that you will take positive or negative

anonymous · Answer

$$
\sin^2(x/2) = \frac{1-\cos(x)}{2} \implies |\sin(x/2)| = \sqrt{\frac{1-\cos(x)}{2}}
$$

anonymous · Answer

$$
x/2 = 7\pi/8 \implies x=7\pi/4
$$

anonymous · Answer

Since $0 \lt x/2\lt \pi$ we know that $\sin$ will be positive.

anonymous · Answer

yes!

anonymous · Answer

It's expected that you know $\cos(7\pi/4)$ because it is a simple angle.

anonymous · Answer

yeaaaa

anonymous · Answer

|dw:1362195597974:dw|

anonymous · Answer

yes...what do i after?

anonymous · Answer

Okay did you find out $\cos(7\pi/4)$?

anonymous · Answer

yes! 1/sqrt2? @wio

anonymous · Answer

It's negative.

anonymous · Answer

oh.:(

anonymous · Answer

Use this formula: $$
\sin(7\pi/8) = \sqrt{\frac{1-\cos(7\pi/4)}{2}}
$$

anonymous · Answer

@wio okay so would that be my answer when i solve for it??

anonymous · Answer

@wio i got -1/2sqrt(1-sqrt2) is this right?

anonymous · Answer

Umm, not sure how you got that.

anonymous · Answer

@wio 
hmmmm -1/2sqrt(2-sqrt2) maybe that's it?

anonymous · Answer

|dw:1362196457353:dw|like this??