If cot Ø = =√15/7 then
tan Ø = -7/√15
you want tangent to be negative and cosine to be positive, ---> must be in IV
construct you triangle in quad IV
by Pythagoras, the hypotenuse is 8
and cos Ø = √15/8
If Cot θ = -Square Root of 15/7, use the fundamental identities to find Cosθ > 0.
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