Question

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

sin five pi divided by twelve

Answer 1

do you mean sin squared \[\sin ^{2}\left( \frac{ 5\Pi }{ 12 } \right)= .5\left( 1-\cos(2\left( \frac{ 5\Pi }{ 12 } \right) \right)\]

Answer 2

i think that is the way to go about it, sorry it took so long

Answer 3

first time using the equation tab

Answer 4

there is soposed to be another " ) " at the end but you get im sure

Answer 5

supposed

Answer 6

its not sin^2 its
\[\sin \frac{ 5\pi }{ 12 }\]
@briensmarandache

Answer 7

@campbell_st can you help?

Answer 8

\[\sin\frac{ 5\pi}{ 12} =(+ or -)\sqrt{\frac{ 1+\cos(\frac{ 5\pi }{ 12 } }{ 2}}\]

Answer 9

doesnt it have to be one half of the 5pi/12 because its the half angle identity

Answer 10

True

Answer 11

So 5pi/24

Answer 12

i think so... now what?

Answer 13

@swagmaster47 what do i do now?

Answer 14

Uhm

Answer 15

\[\sin(5\pi/12) = (+or-)\frac{ \sqrt{1-\cos(5\pi/6)}}{2}\]
which equals

Answer 16

Since sine is positive in quadrant 1
\[\frac{ \sqrt{1+\sqrt(3)/(2)}}{2}\]

Answer 17

I used 5pi/6 as theta since it is an half angle problem

Answer 18

And 5pi/6 is in quadrant 1

Answer 19

my answers can be :
\[1/2 \sqrt{2+\sqrt{3}}\]
\[1/2 \sqrt{2-\sqrt{3}}\]
\[\sqrt{2+\sqrt{3}}\]
\[\sqrt{2-\sqrt{3}}\]

Answer 20

@swagmaster47

Answer 21

1st one

Answer 22

are you sure?

Answer 23

@SolomonZelman what do you think?

Answer 24

My interne cut out, here's my process
\[\frac{ \sqrt{1+\sqrt(3)/(2)} }{ 2 } = \sqrt{2+\sqrt(3)/(4)} = 1/2 \sqrt{2 + \sqrt(3}\]

Answer 25

*internet