Find the values of the trigonometric functions of ? from the information given.

Question

I am so confused how to do this! 

 

Find the values of the trigonometric functions of θ from the information given.
sin(θ) = − 12/13, θ in Quadrant IV

 

cos(θ) =
tan(θ) =
csc(θ) =
sec(θ) =
cot(θ) =

Answer 1

Hi Sydney,

sin(θ) = − 12/13, θ in Quadrant IV

In the fourth quadrant, sinθ <0, tanθ < 0 and cosθ >0

sinθ = opp/hyp, tanθ = opp/adj, and cosθ = adj/hyp

sinθ = -12/13 gives  opp = - 12, and hyp = 13

hpy² = opp² + adj²

(13)² = (-12)² + adj²

169 - 144 = adj²

      ±√25 = adj or adj = ± 5   since cosθ >0 , adj = 5

cos(θ) = adj/hyp = 5/13

tan(θ) = opp/adj =-12/5
csc(θ) = 1/sinθ =1/(-12/13) = -13/12
sec(θ) = 1/cosθ=1/(5/13) =13/5
cot(θ) = 1/tanθ =1/(-12/5)= -5/12