Expert: Scott A Wilson - 4/28/2010

Question
Find the measure of an angle between 0° and 360° that satisfies the condition: cos θ = 0.7815, tan θ < 0

Answer
The numbers were put in Excel, then they were cut from there and pasted here.
That is why there are so many numbers past the decimal.

The cosΘ = 0.7815, so the base angle is 0.673729905 radians, but that is in quadrant 1,
and the tan() of any angle in quadrant 1 is positive.  Here, tan(0.673729905) = 0.798343239.

The other quadrant in which an angle can be found with cosΘ = 0.7815 is quadrant 4.
To find the angle, subtract it from 2π.  This give an angle of 5.609455402 radians.

Just to check, the tan(5.609455402) = -0.798343239, and that is negative.

Perhaps the answer should be rounded to 4 places, since that's what it was given in.