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**amonjezi****Member**- Registered: 2006-03-09
- Posts: 9

hi!

please solve this problem!

sin(36)?

without calculator!

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,626

Seems to be right!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Is 36 degrees or 36 rad?

If it's 36 radians, we get:

IPBLE: Increasing Performance By Lowering Expectations.

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**amonjezi****Member**- Registered: 2006-03-09
- Posts: 9

hi krassi

degrees no radians

thank u

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

thiat used to be one of my high school excercise.

sin36 = 2 sin18 cos18 = 2 cos72 sin72

2 (sin36)^2=8 (cos72)^2 [1- (cos72)^2]

1 - cos72=8 (cos72)^2 [1- (cos72)^2]

cos72=sin18=x

1-x=8 x^2 (1 - x^2) = 8 x^2 (1-x)(1+x) = (1-x)(8 x^2+8 x^3)

x<1, so 8 x^3+8 x^2-1=0

solve it and get sin18, further get cos18, sin36 = 2 sin18 cos18

**X'(y-Xβ)=0**

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