Solve sin &#x2061;<!-- ⁡ --> ( 3 x ) = cos &#x2061;<!-- ⁡ --> ( 2 x ) fo

fetsBedscurce4why1

fetsBedscurce4why1

Answered question

2022-05-17

Solve sin ( 3 x ) = cos ( 2 x ) for 0 x 2 π

Answer & Explanation

Julius Johnston

Julius Johnston

Beginner2022-05-18Added 17 answers

Use sin 3 x = 3 sin x 4 sin 3 x and cos 2 x = 1 2 sin 2 x. To get
3 sin x 4 sin 3 x = 1 2 sin 2 x .
Now call sin x = t. Thus we have
4 t 3 2 t 2 3 t + 1 = 0.
Observe that t=1 is definitely a solution, so we have
( t 1 ) ( 4 t 2 + 2 t 1 ) = 0.
The quadratic factor will be zero for
t = 1 ± 5 4
I hope you can solve from here.
Sappeycuii

Sappeycuii

Beginner2022-05-19Added 3 answers

cos 2 x = sin 3 x = cos ( π 2 3 x )
2 x = 2 m π ± ( π 2 3 x )
where m is any integer
Alternatively,
sin 3 x = cos 2 x = sin ( π 2 2 x )
3 x = n π + ( 1 ) n ( π 2 2 x )
where n is any integer

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