Solve for θ in the equation tan θ = 2.42 when 180° < θ < 360°.

180° < θ < 360° consists of quadrants III and
IV. 

Observing tan θ = 2.42, noticing that 2.47 is a positive number and
realizing that the tangent is only positive in quadrant III, we know that
θ is an angle in quadrant III, so 
180° < θ < 270°

So we use the inverse tangent feature to get 67.54845354°.  But that is NOT 
the answer because 67.54845354° is an angle in quadrant I, not quadrant III.
The value 67.54845354° tells how many degrees θ swings into quadrant III.



So we must add 67.54845354° + 180° and get 247.5484535°.

In the drawing above, the green arc represents the 67.54845354°, which
is the reference angle, and the red arc represents the 247.5484535°. 

Edwin
 

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