Question

Find tan θ if sec θ = square root of twenty six divided by five and sin θ < 0.

Answer 1

hello : sec(θ) = (√26)/5 and: sin (θ) < 0
note : sec(θ) =1/cos(θ)
so : 1/cos(θ) = (√26)/5

cos(θ) = 5/√26
cos²(θ)+sin²(θ)=1
25/26+sin²(θ)=1
sin²(θ)= 1/26
sin(θ)= -(1/√26) ...because : sin θ < 0
tan(θ)= sin(θ)/cos(θ) = -(1/√26) /5/√26 = -1/5