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
