Andreasihf

2022-09-14

Solve the equation $$\mathrm{sin}\pi (2x-3)/6=-0.5$$. Write the smallest positive root for your answer.

Marie Horn

Beginner2022-09-15Added 12 answers

$$\mathrm{sin}\pi (2x-3)/6=-0,5$$

$$\pi (2x-3)/6=-\pi /6+2\pi nU\pi (2x-3)/6=-5\pi /6+2\pi n$$

$$2x-3=-1+12nU2x-3=-5+12n$$

$$2x=2+12nU2x=-2+12n$$

$$x=1+6n,n\in zUx=-1+6n,n\in z$$

Ответ х=1

$$\pi (2x-3)/6=-\pi /6+2\pi nU\pi (2x-3)/6=-5\pi /6+2\pi n$$

$$2x-3=-1+12nU2x-3=-5+12n$$

$$2x=2+12nU2x=-2+12n$$

$$x=1+6n,n\in zUx=-1+6n,n\in z$$

Ответ х=1

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