Given tan Θ = - 8/5 and sin Θ < 0, find sin Θ, cos Θ, csc Θ, sec Θ and cot Θ.

Answer 1

since tangent is negative in II and IV and the sine is negative in III and IV , our angle Ø must be in quadrant IV
so using our given tanØ = -8/5
y = -8, x = 5
and r^2 = 64+25 = 89
r = √89

sinØ = y/r = -8/√89
cosØ = x/r = 5/√89
cscØ = -√89/8
secØ = √89/5
cotØ = -5/8