Formula for \(\displaystyle{\sin{{\left\lbrace{\frac{{\theta}}{{{3}}}}\right\rbrace}}}\) Using \(\displaystyle{\sin{{\left\lbrace{3}\theta\right\rbrace}}}={3}{\sin{{\left\lbrace\theta\right\rbrace}}}-{4}{{\sin}^{{3}}{\left\lbrace\theta\right\rbrace}}\) ,we may



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Formula for sin{θ3}
Using sin{3θ}=3sin{θ}4sin3{θ} ,we may calculate sin{θ3}
But the formula for root of a cubic equation is very complicated can you help me to find a formula for sin{θ3} as it will help to compute sin20,sin10 etc. which will be useful.

Answer & Explanation

Korbin Ochoa

Korbin Ochoa

Beginner2022-03-25Added 11 answers

Using Cardano's method to solve
leads to finding the cube roots of
These are non-real number in general, so you end up using polar form, and so go back to square one.

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