Solving of Trigonometric Ratio using a Pythagorean Identity

Question

If csc θ = 5/3 , how can I find the remaining trigonometric ratio using a Pythagorean Identity?

Answer 1

Assuming that θ is acute

cscθ = 1 / sinθ = 5/3

sinθ = 3/5

cosθ = √(1 - sin²θ) = 4/5

tanθ = sinθ/cosθ = 3/4

secθ = 1/cosθ = 5/4

cotθ = 1/tanθ = 4/3

Answer 2

Let A be the unknown acute angle.

Given that CSC A =5/3 then SIN A = 3/5 b/c they are inverse trip properties. Using the pythagorean theorem we can find the other leg which would be 4.

SIN A = 3/5 CSC A= 5/3

COS A = 4/5 SEC A = 5/4

TAN A= 3/4 COT A = 4/3

Hope this helps.