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0 < x < 360 implies that 0 < 2x < 720

Now,

tan(2x) = sqrt(2)

2x = arctan{sqrt(2)}

2x = 54.74 degrees (to 1 decimal place) is the principal root.

And the other roots are 54.74 + k*180 degrees where k is an integer.

That is, 2x = 54.74, 237.74, 414.74 and 594.74 degrees.

therefore x = 27.37, 117.37, 207.37 and 297.37 degrees.

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9y ago
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Q: How do you solve tan 2x equals root 2 for 0 to 360 degrees?
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