Find the exact value of the following:sin13pi/12 I know i can split it into sin(45+150) but what next???
回答 (3)
2007-12-03 4:48 pm
✔ 最佳答案
according to google sin(13 * pi) / 12 = 0
2007-12-03 4:46 pm
now on i will use @ to represent pi
sin(13@/12) = sin(@/4 + 5@/6)
=sin(@/4)cos(5@/6) + cos(@/4)sin(5@/6)
=1/sqrt2 * -cos(@/6) + 1/sqrt2 * sin(@/6)
=1/sqrt2 * -1/2 + 1/sqrt2 * (sqrt3)/2
= (sqrt(3) -1) / (2*sqrt2)
sin(13@/12) = sin(@/4 + 5@/6)
=sin(@/4)cos(5@/6) + cos(@/4)sin(5@/6)
=1/sqrt2 * -cos(@/6) + 1/sqrt2 * sin(@/6)
=1/sqrt2 * -1/2 + 1/sqrt2 * (sqrt3)/2
= (sqrt(3) -1) / (2*sqrt2)
參考: me
2007-12-03 4:51 pm
I do not know. sin (45)=1/√2. If you split it as
∏+∏/12 , then ∏/12=15 deg, but sin(∏)=0
(a little bit easier). You still have sin(15) which is a fraction.
∏+∏/12 , then ∏/12=15 deg, but sin(∏)=0
(a little bit easier). You still have sin(15) which is a fraction.
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