Proving the closed form of sin &#x2061;<!-- ⁡ --> 48 &#x2218;<!-- ∘ --> </msup>

uznosititr 2022-05-18 Answered
Proving the closed form of sin 48
According to WA
sin 48 = 1 4 7 5 + 6 ( 5 5 )
What would I need to do in order to manually prove that this is true?
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Answers (1)

exhumatql
Answered 2022-05-19 Author has 12 answers
This may be incredibly tedious to do, but you apply the sine sum formula to:
sin ( 48 ) = sin ( 30 + 18 )
Then, sin ( 18 ) and cos ( 18 ) can be computed by using the half angle formulas on sin ( 36 ) and cos ( 36 ), and noting that cos ( 36 ) = 1 2 ϕ, where ϕ = 1 + 5 2 , i.e. the golden ratio.
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