Solving for k in \(\displaystyle{\cos{{\frac{{\pi}}{{k}}}}}-{\cos{{\frac{{{2}\pi}}{{k}}}}}={P}\)

Aryan Salinas

Aryan Salinas

Answered question

2022-04-02

Solving for k in cosπkcos2πk=P

Answer & Explanation

Drahthaare89c

Drahthaare89c

Beginner2022-04-03Added 19 answers

Guide:
cosπk(2cos2πk1)=P
Hence this is a quadratic equation in cosπk
After we solve for the possible values of cosπk ,we can find all possible values for πk and then solve for k.
Jesse Gates

Jesse Gates

Beginner2022-04-04Added 19 answers

cosπkcos2πk=P
cosπk2cos2πk+1=P
Substitute y=cosπk
y2y2=P1
Solve the quadratic equation
2y2y+P1=0

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