How do you solve \sin x\cos x =\frac{1}{2} for x in the interval [0,2

Jaya Legge

Jaya Legge

Answered question

2021-08-16

How do you solve sinxcosx=12 for x in the interval [0,2π)?

Answer & Explanation

dieseisB

dieseisB

Skilled2021-08-17Added 85 answers

sin2x=2sinxcosx
sinxcosx=(12)sin2x=12sin2x=1
sin2x=1arcsin2x=π4x=π4
Check:sinπ4cosπ4=(22)(22)=24=12 Perfect!

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