how to solve angles of trigonometry in general 

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The request of problem is a bit vague since it does not specify if you need to find the angle in a triangle or you just need to find the angle when the value of a trigonmetric function is given.

Considering that the problem provides the value of a trigonometric...

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The request of problem is a bit vague since it does not specify if you need to find the angle in a triangle or you just need to find the angle when the value of a trigonmetric function is given.

Considering that the problem provides the value of a trigonometric function and you just want to know the value of the angle, you need to use the inverse trigonometric functions such that:

`sin alpha = 1/2 => alpha = (-1)^n*arcsin(1/2) + npi`

`alpha = (-1)^n*(pi/6) + npi`

`cos alpha = sqrt2/2 => alpha = +-arccos(sqrt2/2) + 2npi`

`alpha = +-pi/4 + 2npi`

`tan alpha = sqrt3 => alpha = arctan sqrt3 + npi`

`alpha = pi/3 + npi`

`cot alpha = 1 => alpha = arc cot 1 + npi`

`alpha = pi/4 + npi`

Hence, you may evaluate an angle if the value of trigonometric function is given using inverse trigonometric functions and the general relations described in the examples above.

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