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19 votes
19 votes
Giải phương trình sau:
sinx=1/2

User HowlingFantods
by
3.0k points

1 Answer

26 votes
26 votes

Answer:


x = (\pi)/(6) +2\pi k \space , \space \text{for any integer values of } k\\


x = (5\pi)/(6) -2\pi k \space , \space \text{for any integer values of } k\\

Explanation:

Solving with the Periodicity Identity:


\sin(x)= (1)/(2) \\ x = \arcsin((1)/(2)) +2\pi k \\ x = (\pi)/(6) +2\pi k

Solving with the Symmetry Identity:


\sin(x) = (1)/(2) \\ \sin(\pi -x) = (1)/(2) \\ \pi -x = \arcsin((1)/(2)) +2\pi k \\ \pi -x = (\pi)/(6) +2\pi k \\ -x = (\pi)/(6) +2\pi k -\pi \\ -x = (\pi)/(6) - (6\pi)/(6) +2\pi k \\ -x = -(5\pi)/(6) + 2\pi k \\ x = (5\pi)/(6) -2\pi k

User Xorinzor
by
3.0k points
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