Given angle θ, where 0° ≤ θ ≤ 360°, solve for θ to the nearest degree.

Maybe this will help?



To the nearest degree, that is 16.

yes but there's more than one answer, 16 degrees is one of them but there is also 106, 196, and 286

Here are my thoughts:

If the ratio is positive +1.6443, that means there are 2 angles that give this ratio, one that's in the 1st quadrant and one in the 3rd (remember the CAST rule).

Now, we found theta to be 16°, so substituting that into 90 - 2θ:

90 - 2(16) = 58°

58° is an acute angle, so we can use this to find the other hidden angle in quadrant 3:

180 + 58 = 238°

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Using 90 - 2θ, we can solve for yet another theta:

90 - 2θ = 238
238-90 = -2θ
θ = -74

** Unfortunately, we can't use negative angles because of the restrictions given in the question, so we can get its coterminal angles by adding 360 to it, giving use 286°.

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Using the coterminal approach, subtracting 58 minus 360 gives use another hidden angle, -302°.

Using 90 - 2θ, we can solve for yet another theta:

90 - 2θ = -302
-302-90 = -2θ
θ = 196°

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Using the coterminal approach for 238°, subtracting 238° minus 360 gives use another hidden angle, -122°.

Using 90 - 2θ, we can solve for yet another theta:

90 - 2θ = -122
-122-90 = -2θ
θ = 106°

Such an annoying question -- let me know if you need further help

Everything makes sense, except I was confused on why you had to use 58 to subtract from 360, as well as 238.

When you add 360 or subtract 360 from any angle, you get a new angle that will have the same ratio. After finding that tan(58) = 1.6443 and tan(238) = 1.6443, I figured that if I add 360 to 58, I will get 418, and when solving for theta in the expression, it will give me a value between 0 and 360.

An explanation here:

okay, that makes sense, thank you again!