If cos theta= 3/4, what are the possible values of theta in radians?

Answer 1

cos(theta) = 3/4

theta = cos^-1(3/4) = about 41.41 degrees = about 41.41pi/180 = 0.23pi + 2npi radians where n= any integer, in quadrant I

or

in quadrant IV, theta = about -.23pi or (2-.23)pi = 1.73pi +2npi radians where n= any integer,

or about 1.73(3.14) = 5.43 + 18.84n radians where n= any integer, in quadrant IV

and about .23(3.14) = 0.72 + 18.84n radians where n= any integer, in quadrant I

which are equivalent to about 41.41 + 360n degrees where n= any integer

and about 318.59 + 360n degrees, where n = any integer

or theta = 41.41 or 0.72 or .23pi in Quadrant I

or 318.59 or 5.43 or 1.73pi in Quadrant IV

all with either 360n or 2pin where n= any integer

there are an infinite number of angles = theta where cos(theta) = 3/4

for just radians, with smallest positive solutions: 0.72 or 5.43, approximately