Question

Find tan θ if cos θ = 1/4 and sin θ < 0.

Answer 1

Hello : 
cos²(θ) +sin²(θ) = 1
(1/4)² +sin²(θ) = 1
sin²(θ) = 1 -1/16
sin²(θ) =15/16
sin(θ) = - √(15/16)=- √15/4    because : sin θ < 0.
tan (θ) =sin (θ)/  cos( θ) =(- √15/4)/(1/4) = - √15