find cosx and cotx if sinx = 1/4 and tanx < 0

Answer 1

tangent is negative and sine is positive in quadrant 2

so opposite =1 and hypotenuse = 4

then adjacent is - sqrt( 4^2 - 1^2) = - sqrt(16-1) = -sqrt(15)

so cosine is -sqrt(15)/4

then tangent is -1/sqrt(15) = -sqrt(15)/15

cosecant is 4, secant is -4/15 * sqrt(15), and cotangent is -sqrt(15)