The general solution for the equation sin2x = 0.5 is derived using the arcsine function and the properties of sine. The solutions are x = 15 degrees + k180 and x = 75 degrees + k180, where k is any integer. It is crucial to recognize that using arcsine can lead to missing solutions in the second quadrant, which is addressed by considering both 30 degrees and 150 degrees as potential angles for 2x. The complete solution includes both forms: 2x = arcsin(0.5) + 2kπ and 2x = π - arcsin(0.5) + 2kπ.
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GrandMaster87 said:Homework Statement
Solve for x using general solution
sin2x = 0.5
Homework Equations
sin2x= 2sinxcosx
The Attempt at a Solution
arcsin0.5 = 2x
2x = 30 degrees + k360
x = 15 degrees + k180.
Or
2x = (180-30) + k360
2x = 150 + k360
x = 75 + k180