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This problem trains for: AMC-10, SAT-II, AMC-12.

Solve the equation:

equation

Which one of the following angles is closest to a solution?

Use the unit circle to verify that:

equation

equation

figure

Therefore, the equation becomes:

equation

equation

equation

equation

equation

We use the substitution:

equation

The equation becomes quadratic in t with the roots:

equation

However, only one of the roots is in the range of the sine function:

equation

with a solution for x in the principal period of the sine function:

equation

However, other solutions exist due to the periodicity of the sine function. The next largest positive angle that satisfies is close to:

equation

We notice that 141° is closest to a solution.

figure