Verified answer

sin 165

= sin (180- 15)

= sin 180 cos 15 - cos 180 sin 15

= 0 (cos 15) - (-1)(sin 15)

= 0 + sin 15

= sin 15

= sin (30/2)

= sqrt [(1 - cos 30)/2]

= sqrt [(1 - (sqrt 3)/2) /2 ]

= sqrt [(2 - sqrt 3)/2)/2]

= sqrt [(2 - sqrt 3)/4]

= (1/2) sqrt (2 - sqrt 3)

The exact value of sin 165 degrees is "0.25881904510252076234889883762405"

ooh! a bit long

you seem to have the same question as lana l. so I'm just going to copy my answer for her question...

Note that the difference between 165 degrees and 180 degrees is 15 degrees.

so, you can say that you are actually computing for sin 15

sin 15 can be expressed as sin (30/2) allowing us to use the trig identity:

sin (x/2) = sqrt [(1- cos x)/2]

sqrt [(1 - cos 30)/2]

Recall the 30-60-90 triangle/rule...

sqrt [(1 - (sqrt3)/2 )/2]

so that's your answer. If don't know if you can still simplify this further, though.

165= 45+120 = pi/2 + 4pi/3

sin (u+v)= sin u cosv + sinv cosu

sin ( pi/2 + 4pi/3 ) = [-(sqrt 2) / 4] + [(sqrt 6) / 4] = [(sqrt 6)-(sqrt 2) / 4] = 0.2588

Heather's answer is wrong by the way

Nevermind, it isn't wrong. It's just more complicated. Pick me, pick me!! =p

sin(165) = 0.997797279

using the google search engine by just typing in sin(165)

Use your calculator.

0.25881904510252076234889883762405