The smallest positive solution of tan bx = 2 is x = 0.3. Determine the general solution of tan bx = 2.

The general solution of and is , .

From Trigonometry we remember that Tangent is a Transcendental Function that is positive both in 1st and 3rd Quadrants and have a periodicity of radians.  The procedure consists in using concepts of Direct and Inverse Trigonometric Functions as well as characteristics related to the behavior of the tangent function in order to derive a General Formula for every value of , measured in radians.

First, we solve the following system of equations for :

(1)

(2)

Please notice that angles are measured in radians.

(2) in (1):

Under the assumption of periodicity, we know that:

,

If we know that and , then the general solution of this trigonometric function is:

,

,

The general solution of and is , .

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step-by-step explanation:

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