how do you find algebraically the measure of the obtuse angle, to the nearest degree, that satisfies the equation 3 sec theta = 5
is it sec theta = 5/3 and then cos -1 (5/8) = 0.4
3secØ = 5
secØ = 5/3
then cosØ = 3/5 , since secA = 1/cosA
Ø = arccos 3/5 = appr53.13°
but you wanted the obtuse angle, so
Ø = 360-53.13 = 306.87° , because the cosine is positive in quadrant I and IV
to the nearest degree it would be 307°