Find cos0 if tan0 = 5 and sin0 < 0

Question

Find cos0 if tan0 = 5 and sin0 < 0

Answer 1

tanT = 5, sin0 <0, tanT <0 in quadrant IV

tanT = opposite side/adjacent side = 5/1

hypotenuse squared = opposite^2 + adjacent^2= 25+1 = 26

hypotenuse = sqr26

cosT = adjacent side/hypotenuse = 1/sqr26 (sqr26)/26 = about 0.1961...

= about 1/5

cosines are all >0 in quadrant IV

Answer 2

tanθ = 5; sinθ < 0, so θ in quadrant IV.

cosθ = 1/√1 + 25 = 1/√26