How do you solve sin⁡2x=sin⁡x?

Salvatore Boone

Salvatore Boone

Answered

2021-12-24

How do you solve sin2x=sinx?

Answer & Explanation

Philip Williams

Philip Williams

Expert

2021-12-25Added 39 answers

sin2x=sinx
2sinxcosx=sinx
2sinxcosxsinx=0
sinx(2cosx1)=0
Solution A: sinx=0x=kπ,kZ
Solution B: 2cosx=1cosx=12,x=±π3+2kπ=π3+2kπ=π3(6k±1), kZ
x=kπ or x=π3(6k±1),kZ
Paineow

Paineow

Expert

2021-12-26Added 30 answers

Factor sin(x) out of 2sin(x)cos(x)sin(x)
sin(x)(2cos(x)1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
sin(x)=0
2cos(x)1=0
Set the first factor equal to 0 and solve.
x=2πn,π+2πn for any integer n
Set the next factor equal to 0 and solve.
x=π3+2πn, for any integer n
The final solution is all the values that make sin(x)(2cos(x)1)=0 true.
x=2πn,π+2πn,π3+2πn,5π3+2πn, for any integer n
The finall solution is all the values that make sin(x)(2cos(x)1)=0 true.
x=2πn,π+2πn,π3+2πn,5π3+2πn, for any integer n
Consolidate 2πn and π+2πn to πn
x=πn,π3+2πn,5π3+2πn for any integer n
user_27qwe

user_27qwe

Expert

2021-12-30Added 230 answers

Very good answer

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