Question

g if cot=-1/3 and sin<0 find each function value only using the appropriate trigonometric identites

Answer 1

Explanation:

Other trigonometry identities that we have includes cosθ, sinθ, tanθ, secθ, cosecθ

cosecθ = 1/sinθ

Given cotθ=-1/3 and sinθ<0, this means that θ falls in the 4th quadrant.

cotθ= 1/tanθ = -1/3

tanθ = -3/1

Since tanθ = opposite/adjacent = -3/1

opposite = -3

adjacent = 1

Using pythagoras theorem to get the hypotenuse, hyp² = opp²+adj²

hyp² = (-3)²+1²

hyp = √9+1

hyp = √10

cosθ = adjacent/hypotenuse = 1/√10

sinθ = opp/hyp = -3/√10

cosecθ = 1/sinθ = 1/(-3/√10)

cosecθ = -√10/3

secθ = 1/cosθ

secθ = 1/(1/√10)

secθ = 1*√10/1

secθ = √10