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General Solution

Sine Function

Cosine Function

Tangent Function

Trigonometric Equations

Quiz

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Tangent Function

Say we are given the equation tan x = k, where k is constant. Graphically, this equation is illustrated as such (in radians):

The black dots indicate the co-ordinates of a solution. As you can see, there are infinitely many solutions, 3 of which are illustrated in the graph.

The general solution is given by:

                         q = np + tan^-1k 

or, in degrees,        q = 180^on + tan^-1k

Note: tan^-1k must be in the principal range, between -p/2 and p/2.

Example: Find the general solution of tan (2x + 30^o) = 1

Solution: