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

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