put that in a fraction please.... ;)
2007-03-22 04:32:20 · 7 answers · asked by jakw w 1 in Science & Mathematics ➔ Mathematics
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)
2007-03-22 04:45:32 · answer #1 · answered by Mathematica 7 · 3⤊ 1⤋
The exact value of sin 165 degrees is "0.25881904510252076234889883762405"
ooh! a bit long
2007-03-22 12:04:27 · answer #2 · answered by Anonymous · 0⤊ 1⤋
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.
2007-03-22 11:41:20 · answer #3 · answered by trauma53 2 · 2⤊ 1⤋
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
2007-03-22 11:49:05 · answer #4 · answered by piri82 3 · 0⤊ 0⤋
sin(165) = 0.997797279
using the google search engine by just typing in sin(165)
2007-03-22 12:04:37 · answer #5 · answered by Crap_At_Maths 2 · 0⤊ 1⤋
Use your calculator.
2007-03-22 11:43:52 · answer #6 · answered by mohamed g 1 · 0⤊ 3⤋
0.25881904510252076234889883762405
2007-03-22 11:36:32 · answer #7 · answered by Fbfbfbfb 2 · 0⤊ 3⤋