Question

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

Answer 1

\(\frac{7\pi}{8}\) is half of \(\frac{7\pi}{4}\) so use the half angle formula for this one

Answer 2

\[\sin(\frac{x}{2})=\pm\sqrt{\frac{1-\sin(x)}{2}}\] replace \(\sin(x)\) by \(\sin(\frac{7\pi}{4})\)

Answer 3

@Hyun11 it does use latex, that is how you write here

Answer 4

if you want to see the code, right click and choose "show math as" then "latex"
you seem very angry
relax

Answer 5

so \[\sin (7\pi/4)/2)?\]

Answer 6

no
do you know what \(\sin(\frac{7\pi}{4})\) is ?

Answer 7

The argument of trigonometric functions can be reduced modulo \[2\pi\]

Answer 8

first find \(\sin(\frac{7\pi}{4})\) then replace that in the half angle formula here \[\sin(\frac{x}{2})=\pm\sqrt{\frac{1-\sin(x)}{2}}\]

Answer 9

Write \[\frac{7\pi}{4}=\frac{8\pi}{4}-\frac{\pi}{4}=2\pi-\frac{\pi}{4}\]

Answer 10

forget about "modulo \(2\pi\) " as \(\frac{7\pi}{4}<2\pi\)

Answer 11

look at the unit circle, you will see that
\[\sin(\frac{7\pi}{4})=-\frac{\sqrt{2}}{2}\]

Answer 12

Yeah so \[\sqrt{(1-7\pi/4)/2}\]

Answer 13

then use the formula i wrote above

Answer 14

no
where you have \(\frac{7\pi}{4}\) you should have \(-\frac{\sqrt{2}}{2}\)

Answer 15

ok then what?

Answer 16

\[\sin(\frac{x}{2})=\pm\sqrt{\frac{1-\sin(x)}{2}}\]
\[\sin(\frac{7\pi}{8})=\pm\sqrt{\frac{1-\sin(\frac{7\pi}{4})}{2}}\]
=\[\pm\sqrt{\frac{1+\frac{\sqrt2}{2}}{2}}\]

Answer 17

\[\sqrt{(1+2\pi/2})/2\]

Answer 18

take a look at the answer i wrote above

Answer 19

oh wait forget the pi >.<

Answer 20

soo \[\sqrt{2-\sqrt{2}/2}\]?

Answer 21

should be a plus sign inside the radical

Answer 22

also there should be a minus sign outside of the whole thing, because \(\frac{7\pi}{8}\) is in quadrant 3 and therefore the sine is negative