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

Polchinio3es

Polchinio3es

Answered question

2022-03-24

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
3s4s3=sint
leads to finding the cube roots of
±1sin2t+isint=±cost+isint=±eit
These are non-real number in general, so you end up using polar form, and so go back to square one.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?