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This problem trains for: AMC-10, SAT-II, AMC-12.
Solve the equation:
Which one of the following angles is closest to a solution?
Use the unit circle to verify that:
Therefore, the equation becomes:
We use the substitution:
The equation becomes quadratic in t with the roots:
However, only one of the roots is in the range of the sine function:
with a solution for x in the principal period of the sine function:
However, other solutions exist due to the periodicity of the sine function. The next largest positive angle that satisfies is close to:
We notice that 141° is closest to a solution.