Solve (in radians) sec x = 2csc x

When I work it out, it gets to
2cot x - 1 = 0
cot x = 1/2

Would it be ok to use tan^-1 (2) ? I must demonstrate it with a graph as well... would the line go through Q I/III or II/IV ? Thank you!

1 answer

sec x = 2csc x
1/cosx = 2/sinx
sinx = 2cosx

sinx/cosx = 2
tanx = 2

yes, I would use tan^-1 (2), but make sure your calculator is set to radians, (DRG key)

Also remember that the tangent is positive in quads I and III
tan^-1 (2) = appr 1.107
x = 1.107 or x = π+1.107= appr 4.249