Use the values sec x = - 3/2 and tan x > 0

Answer 1

sec(x) = -3/2 // given

cos(x) = -2/3 // reciprocal of sec(x)

x= cos^-1(-2/3) ≈ 2.3005 & 3.9827

tan(x) > 0 // meaning the angle x is either in quadrant I or III because that is where tan(x) is positive

2.3005 radians is located in Quadrant II

3.9827 is located in Quadrant III

so the angle x ≈ 3.9827