Answer:
secθ = 17/15
Step-by-step explanation:
From the information given,
Cosθ = 15/17
The right triangle representing this angle is shown below
Considering right triangle ABC in the figure,
hypotenuse = AC = 17
Adjacent side = AB = 15
Opposite side = BC
We would find BC by applying the pythagorean theorem which is expressed as
hypotenuse^2 = opposite side^2 + adjacent side^2
Thus,
17^2 = BC^2 + 15^2
289 = BC^2 + 225
BC^2 = 289 - 225 = 64
BC = √64
BC = 8
BC is in the negative y axis, Thus,
opposite side = BC = - 8
Recall, θ is in the 4th quadrant
Sinθ = opposite side/hypotenuse
Sin is negative in the 4th quadrant
Thus,
Sinθ = - 8/17
cscθ = 1/Sinθ = - 17/8
tanθ = opposite side/adjacent side
tanθ =
secθ = 1/cosθ = 1/(15/17) = 1 x 17/15
secθ = 17/15
Cosθ = adjacent side/hypotenuse