Question

Giải phương trình sau:
sinx=1/2

Answer 1

`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`