Raymond B. answered 05/21/24
Math, microeconomics or criminal justice
tanx = 4/11 tanx>0 means x is in quadrant 1 or 3
secx<0 means x is in quadrant 2 or 3
so x is in quadrant 3
tanx = 4/11 = opposite/adjacent with hypotenuse = sqr(16+121) =sqr137
cosx = adjacent/hypotenuse = 11/-sqr137, sinx = opposite/hypotenuse = 4/-sqr137
cos2x = cos^2(x)-sin^2(x)= 121/137 - 16/137= (121-16)/137 = 105/137
cos2x =105/137= about 0.7664234
x is in quadrant 3,
2x is in quadrant 1
check the answer using a calculator with inverse trig functions
x= arctan(4/11)= about 19.983 degrees or 180+19.983 = 199.983
2x=39.966 or 399.966 degrees
cos2x=cos39.966 = about .766426 or cos399.966 =cos(399.966-360) = cos39.966 = .766426
close enough
actually the secant sign is irrelevant to finding cos2x,but not to finding x or 2x