Solve the equation.\sin 3x=1, 0\geq x< 2\pi

Tazmin Horton

Tazmin Horton

Answered question

2021-09-15

Solve the equation.
sin3x=1,0x<2π

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-09-16Added 92 answers

Step 1
Here , we use the result shown on board.
sin0=10=π2+2nπ,nI
Step 2
For different values of n( where n is integers), we get different solutions of trignometric equation. But only for n=0,1,2, we get solution in [0,2π)
sin3x=1
3x=π2+2nπ,nI
x=π6+23nπ,nI
n=0,x=π6
n=1,x=π6+2π3=5π6
n=2,x=π6+4π3=9π6=3π2
Step 3
Result:
x=π6,5π6,3π2

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